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JH

# (a) Find the partial sum $s_10$ of the series $\sum_{n = 1}^{\infty} 1/n^4.$ Estimate the error in using $s_10$ as an approximation to the sum of the series.(b) Use (3) with $n = 10$ to give an improved estimate of the sum.(c) Compare your estimate in part (b) with the exact value given in Exercise 35. (d) Find a value of $n$ so that $s_n$ is within 0.00001 of the sum.

## a) 0.000$\overline{3}$b) $s \approx 1.082328$c) 0.0000053d) $n=33$ terms for the required accuracy

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

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