(i) Let be the statement 1^ 4 +2^ 4 +3^ 4 + +n^ 4 = n(n+1)(2n+1)(3n^ 2 +3n-1) 30 .…

MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof

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}