Integral Test

Calculus Level 3

Using the integral test, find the best possible estimation for the series n=11n3\displaystyle\sum_{n=1}^\infty \frac{1}{n^3} using a partial sum with 1010 terms.

Note that n=1101n31.19753 \displaystyle\sum_{n=1}^{10} \frac{1}{n^3} \approx 1.19753 and 11120.00826\tfrac{1}{11^2} \approx 0.00826.

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