Search results
Results From The WOW.Com Content Network
In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann . One very common application is in numerical integration , i.e., approximating the area of functions or lines on a graph, where it is also known as the rectangle rule .
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
The sum of the members of a finite arithmetic progression is called an arithmetic series. For example, consider the sum: For example, consider the sum: 2 + 5 + 8 + 11 + 14 = 40 {\displaystyle 2+5+8+11+14=40}
The sum of a finite initial segment of an infinite geometric series is called a finite geometric series, that is: [2] + + + + + = =. When r > 1 {\displaystyle r>1} it is often called a growth rate or rate of expansion.
Total the values: Sum up the values of all your personal property to get the total value of your belongings. This figure represents the estimated value of your personal property.
However, if the terms and their finite sums belong to a set that has limits, it may be possible to assign a value to a series, called the sum of the series. This value is the limit as n {\displaystyle n} tends to infinity of the finite sums of the n {\displaystyle n} first terms of the series if the limit exists.
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1] ¯ = ().
Abel's summation formula can be generalized to the case where is only assumed to be continuous if the integral is interpreted as a Riemann–Stieltjes integral: ∑ x < n ≤ y a n ϕ ( n ) = A ( y ) ϕ ( y ) − A ( x ) ϕ ( x ) − ∫ x y A ( u ) d ϕ ( u ) . {\displaystyle \sum _{x<n\leq y}a_{n}\phi (n)=A(y)\phi (y)-A(x)\phi (x)-\int _{x ...