The geometric series converges to

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The geometric series

\displaystyle \sum_{k=0}^{\infty} 5\left(\tfrac14\right)^k

converges to

S=\dfrac{20}{3}

. Determine the least integer

N

such that

|S-S_N|<0.01