a.) Compute $S_{4}$ (the 4th partial sum) of the following series. $$S=\sum_{n=1}^{\infty}\frac{3}{6 n^3}$$
Answer:

b.) Estimate the error in using $S_{4}$ as an approximation of the sum of the series. (i.e. use $\int_{4}^{\infty} f(x)\, dx \geq R_{4}$ )

Answer:

c.) Use $n = 4$ and $$S_n + \int_{n+1}^{\infty} f(x)\, dx \leq S \leq S_n + \int_{n}^{\infty}f(x)dx$$ to find a better estimate of the sum.

Answer: $\leq S \leq$

Note: the answers in the last part are tested to high precision.