$(a)$ Compute $s_{6}$ of $\displaystyle \sum_{n=1}^\infty\frac{3}{6 n^4}$

$(b)$ Estimate the error in using $s_{6}$ as an approximation of the sum of the series. (I.e. use $\displaystyle \int_{6}^{\infty} f(x)dx \geq r_{6}$)

$(c)$ Use n = 6 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.
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