a) Prove that the sum of fourth powers of the first n integers is 1/30n(n+1) (2n+1)(3n2+3n+1) .
Please explain
Hello, spmlingam!
You have a typo . . .
Prove that the sum of fourth powers of the first $\displaystyle n$ integers is:
. . . . . . . . . . . . . . . . . . $\displaystyle {\color{red}\downarrow}$
. . $\displaystyle \frac{n(n+1) (2n+1)(3n^2+3n{\bf{\color{red}-}}1)}{30}$
An inductive proof may be the way to go.
. . [The algebra gets very messy, though.]
Any other approach requires even more algebra . . .