Page 172 - 'Blast_Into_Math

Blast into Math! Analatic nummer theora: ants, ghosts and giants

Definition 7.1.3 Let

∞
{x n } n=1

be a sequence of real numbers. The N partial sum is
th
N

S N = x n = x 1 + x 2 + ... + x N .
n=1

This is the sum of all the terms in the sequence beginning with the first term up to the N th term. If the
sequence of partial sums

{S N} N =1
∞

converges to a limit L, then we say that the series converges to L , and we write

∞

x n = L.
n=1

The Marching Ant Proposition can help us determine whether or not a series converges.

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