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symsum

Sum of series

Syntax

Description

example

symsum(expr,var) evaluates the sum of a series, where expression expr defines the terms of a series, with respect to the symbolic variable var. The value of the variable var changes from 0 to var - 1. If you do not specify the variable, symsum uses the default variable determined by symvar. If expr is a constant, then the default variable is x.

example

symsum(expr,var,a,b) evaluates the sum of a series, where expression expr defines the terms of a series, with respect to the symbolic variable var. The value of the variable var changes from a to b. If you do not specify the variable, symsum uses the default variable determined by symvar. If expr is a constant, then the default variable is x.

symsum(expr,var,[a,b]), symsum(expr,var,[a b]), and symsum(expr,var,[a;b]) are equivalent to symsum(expr,var,a,b).

Examples

Evaluate the Sum of a Series

Evaluate the sum of a series for the symbolic expressions k and k^2:

syms k
symsum(k)
symsum(1/k^2)
ans =
k^2/2 - k/2

ans =
-psi(1, k)

Evaluate the Sum of a Series Specifying Bounds

Evaluate the sum of a series for these expressions specifying the bounds:

syms k
symsum(k^2, 0, 10)
symsum(1/k^2,1,Inf)
ans =
385
 
ans =
pi^2/6

You also can specify bounds as a row or column vector:

syms k
symsum(k^2, [0, 10])
symsum(1/k^2, [1; Inf])
ans =
385
 
ans =
pi^2/6

Evaluate the Sum of a Series Specifying the Summation Index and Bounds

Evaluate the sum of a series for this multivariable expression with respect to k:

syms k x
symsum(x^k/sym('k!'), k, 0, Inf)
ans =
exp(x)

Input Arguments

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expr — Expression defining terms of seriessymbolic expression | symbolic function | symbolic vector | symbolic matrix | symbolic number

Expression defining terms of series, specified as a symbolic expression or function, a constant, or a vector or matrix of symbolic expressions, functions, or constants.

var — Summation indexsymbolic variable

Summation index, specified as a symbolic variable. If you do not specify this variable, symsum uses the default variable determined by symvar(expr,1). If expr is a constant, then the default variable is x.

a — Lower bound of summation indexnumber | symbolic number | symbolic variable | symbolic expression | symbolic function

Lower bound of summation index, specified as a number, symbolic number, variable, expression or function (including expressions and functions with infinities).

b — Upper bound of summation indexnumber | symbolic number | symbolic variable | symbolic expression | symbolic function

Upper bound of summation index, specified as a number, symbolic number, variable, expression or function (including expressions and functions with infinities).

More About

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Definite Sum

The definite sum of series is defined as

Indefinite Sum

is called the indefinite sum of xi over i, if the following identity is true for all values of i:

    Note:   symsum does not compute indefinite sums.

See Also

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Related Examples

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