
sum to infinity


The value that the sum of the first n terms of a convergent series approaches as n approaches infinity.
For example, assume that S_{n} = 1/2 + 1/2^{2} + 1/2^{3} + . . . + 1/2^{n} Hence, 2S_{n} = 1 + 1/2^{1} + 1/2^{2} + . . . + 1/2^{n1} Therefore, we have 2S_{n}  S_{n} = 1  1/2^{n} S_{n} = 1  1/2^{n} Let n approach infinity, 1/2^{n} approaches zero and the sum of the first n terms approaches 1.

