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

Hence,

   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.

Related Term: convergent series


 
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