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
Sn = 1/2 + 1/22 + 1/23 + . . . + 1/2n
2Sn = 1 + 1/21 + 1/22 + . . . + 1/2n-1
Therefore, we have
2Sn - Sn = 1 - 1/2n
Sn = 1 - 1/2n
Let n approach infinity, 1/2n approaches zero and the sum of the first n terms approaches 1.