The series is approximated by its fifth partial sum

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The series ∑n=1∞(−1)n+12n2\displaystyle \sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{2}{n^{2}} is approximated by its fifth partial sum, which is S5≈1.463611S_5\approx1.463611. What is the greatest possible distance between S5S_5 and the true value of the series? (a) 0.0408160.040816 (b) 0.0800000.080000 (c) 0.0555560.055556 (d) 0.0277780.027778

Related theory

Browse the problem library