Examples for

Sums

Summation is the addition of a list, or sequence, of numbers. If the summation sequence contains an infinite number of terms, this is called a series. Sums and series are iterative operations that provide many useful and interesting results in the field of mathematics.
Finite Sums

Compute a finite summation of a mathematical expression.

Compute an indexed sum:

sum j^2, j=1 to 100
sum x^k, k=0 to n

Sum an incompletely specified sequence of terms:

1+2+3+...+10
3+12+27+...+300
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Infinite Sums

Find the sum of an infinite number of terms.

Compute an infinite sum:

sum 1/n^2, n=1 to infinity
sum x^k/k!, k=0 to +oo

Sum a geometric series:

sum (3/4)^j, j=0..infinity
sum x^n, n=0 to +oo

Compute a sum over all integers:

sum 1/(1+n^2), n=-oo to +oo

Compute an infinite sum (limits unspecified):

sum 1/n^2

Sum an incompletely specified infinite series:

1/2 + 1/4 + 1/8 + 1/16 + ...
1/2^2 + 1/3^2 + 1/5^2 + 1/7^2 + ...
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Sum Convergence

Explore the behavior of series, in particular whether or not they converge to a particular value.

Determine if an infinite sum converges:

sum convergence of n
sum convergence of n^(-2)
does the sum of 2^(-n) converge
does the sum of 5*3^(1 - n) converge
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