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Geometric Sum
In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant. For example, the series \tfrac12 + \tfrac14 + \tfrac18 + \cdots is a geometric series with common ratio , which converges to the sum of . Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same way that each term of an arithmetic series is the arithmetic mean of its neighbors. While Greek philosopher Zeno's paradoxes about time and motion (5th century BCE) have been interpreted as involving geometric series, such series were formally studied and applied a century or two later by Greek mathematicians, for example used by Archimedes to calculate the area inside a parabola (3rd century BCE). Today, geometric series are used in mathematical finance, calculating areas of fractals, and various computer science topics. Though geometric series most commonly involve real or compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field (mathematics)
In mathematics, a field is a set (mathematics), set on which addition, subtraction, multiplication, and division (mathematics), division are defined and behave as the corresponding operations on rational number, rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as field of rational functions, fields of rational functions, algebraic function fields, algebraic number fields, and p-adic number, ''p''-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many element (set), elements. The theory of fields proves that angle trisection and squaring the circle cannot be done with a compass and straighte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interest Rate
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized. The interest rate has been characterized as "an index of the preference . . . for a dollar of present ncomeover a dollar of future income". The borrower wants, or needs, to have money sooner, and is willing to pay a fee—the interest rate—for that privilege. Influencing factors Interest rates vary according to: * the government's directives to the central bank to accomplish the government's goals * the currency of the principal sum lent or borrowed * the term to m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate Of Return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return. A loss instead of a profit is described as a '' negative return'', assuming the amount invested is greater than zero. To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the rate of return. Typically, the period of time is a year, in which case the rate of return is also called the annualized return, and the conversion process, described below, is called ''annualiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Investment
Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broader viewpoint, an investment can be defined as "to tailor the pattern of expenditure and receipt of resources to optimise the desirable patterns of these flows". When expenditures and receipts are defined in terms of money, then the net monetary receipt in a time period is termed cash flow, while money received in a series of several time periods is termed cash flow stream. In finance, the purpose of investing is to generate a Return (finance), return on the invested asset. The return may consist of a capital gain (profit) or loss, realised if the investment is sold, unrealised capital appreciation (or depreciation) if yet unsold. It may also consist of periodic income such as dividends, interest, or rental income. The return may also inclu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Value (economics)
In economics, economic value is a measure of the benefit provided by a goods, good or service (economics), service to an Agent (economics), economic agent, and value for money represents an assessment of whether financial or other resources are being used effectively in order to secure such benefit. Economic value is generally measured through units of currency, and the interpretation is therefore "what is the maximum amount of money a person is willing and able to pay for a good or service?” Value for money is often expressed in comparative terms, such as "better", or "best value for money", but may also be expressed in absolute terms, such as where a deal does, or does not, offer value for money. Among the competing schools of economic theory there are differing Theory of value (economics), theories of value. Economic value is ''not'' the same as Price, market price, nor is economic value the same thing as market value. If a consumer is willing to buy a good, it implies tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deflation
In economics, deflation is a decrease in the general price level of goods and services. Deflation occurs when the inflation rate falls below 0% and becomes negative. While inflation reduces the value of currency over time, deflation increases it. This allows more goods and services to be bought than before with the same amount of currency. Deflation is distinct from '' disinflation'', a slowdown in the inflation rate; i.e., when inflation declines to a lower rate but is still positive. Economists generally believe that a sudden deflationary shock is a problem in a modern economy because it increases the real value of debt, especially if the deflation is unexpected. Deflation may also aggravate recessions and lead to a deflationary spiral . Some economists argue that prolonged deflationary periods are related to the underlying technological progress in an economy, because as productivity increases ( TFP), the cost of goods decreases. Deflation usually happens when supply is hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inflation
In economics, inflation is an increase in the average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduction in the purchasing power of money. The opposite of CPI inflation is deflation, a decrease in the general price level of goods and services. The common measure of inflation is the inflation rate, the annualized percentage change in a general price index. Changes in inflation are widely attributed to fluctuations in Real versus nominal value (economics), real demand for goods and services (also known as demand shocks, including changes in fiscal policy, fiscal or monetary policy), changes in available supplies such as during energy crisis, energy crises (also known as supply shocks), or changes in inflation expectations, which may be self-fulfilling. Moderat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Level
The general price level is a hypothetical measure of overall prices for some set of goods and services (the consumer basket), in an economy or monetary union during a given interval (generally one day), normalized relative to some base set. Typically, the general price level is approximated with a daily price ''index'', normally the Daily CPI. The general price level can change more than once per day during hyperinflation. Theoretical foundation The classical dichotomy is the assumption that there is a relatively clean distinction between overall increases or decreases in prices and underlying, “nominal” economic variables. Thus, if prices ''overall'' increase or decrease, it is assumed that this change can be decomposed as follows: Given a set C of goods and services, the total value of transactions in C at time t is :\sum_ (p_\cdot q_)=\sum_ P_t\cdot p'_)\cdot q_P_t\cdot \sum_ (p'_\cdot q_) where :q_\, represents the quantity of c at time t :p_\, represents the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyses what is viewed as basic elements within economy, economies, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyses economies as systems where production, distribution, consumption, savings, and Expenditure, investment expenditure interact; and the factors of production affecting them, such as: Labour (human activity), labour, Capital (economics), capital, Land (economics), land, and Entrepreneurship, enterprise, inflation, economic growth, and public policies that impact gloss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Progression
A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the ''common ratio''. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers ''r''''k'' of a fixed non-zero number ''r'', such as 2''k'' and 3''k''. The general form of a geometric sequence is :a,\ ar,\ ar^2,\ ar^3,\ ar^4,\ \ldots where ''r'' is the common ratio and ''a'' is the initial value. The sum of a geometric progression's terms is called a '' geometric series''. Properties The ''n''th term of a geometric sequence with initial value ''a'' = ''a''1 and common ratio ''r'' is given by :a_n = a\,r^, and in general :a_n = a_m\,r^. Geometric sequences satisfy the linear recurrence relation :a_n = r\,a_ f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
