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 $\tfrac{1}{11^2} \approx 0.00826$ .

Value 1.19753, error at most 0.01 Value 1.20666, error at most 0.00087 Value 1.2021, error at most 0.00044 Value 1.20753, error at most 0.00413 Value 1.19753, error at most 0.00826