Prove that j4 = n(n + 1)(2 n + 1)(3 n2 + 3 n ?1)/30

Chapter 5, Problem 17E

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Prove that $\sum_{j=1}^{n} j^{4}=n(n+1)(2 n+1)\left(3 n^{2}+3 n-1\right) / 30$ whenever $n$ is a positive integer.

Equation Transcription:

$\sum\limits_{j\ =1}^{n}\ {j}^{4}\ =\ n(n\ +1)\ (2n\ +1)(3{n}^{2}\ +\ 3n\ -1)/30$

$n$

Text Transcription:

sum_{j=1}^{n} j^{4}=n(n+1)(2 n+1)(3 n^{2}+3 n-1) / 30

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