Mathematics

Problem

(i) Let

P(n)

be the statement

1^{4}+2^{4}+3^{4}+\dots+n^{4}=\frac{n(n+1)(2n+1)(3n^{2}+3n-1)}{30}.

Prove that

P(n)

is true for every positive integer

n

. (ii) Using the result proved in part (i), find the value of

1^{4}+2^{4}+\dots+10^{4}