Integral Test

Calculus Level 3

Using the integral test, find the best possible estimation for the series \(\displaystyle\sum_{n=1}^\infty \frac{1}{n^3}\) using a partial sum with \(10\) terms.

Note that \( \displaystyle\sum_{n=1}^{10} \frac{1}{n^3} \approx 1.19753 \) and \(\tfrac{1}{11^2} \approx 0.00826\).