Calculate the 4th partial sum of the series

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

Problem

Calculate the 4th partial sum

S_4

of the series

\displaystyle \sum_{n=0}^{\infty} \left(\tfrac{1}{3}\right)^{n}

, and state the absolute error between

S_4

and the exact sum of the series.