Consider the alternating geometric series

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

\displaystyle \sum_{k=0}^{\infty} (-1)^k 2^{-(k+1)}

, whose sum is

S=\tfrac{1}{3}

. Find the least integer

N

such that

|S-S_N|<2\times10^{-4}