# Thread: [SOLVED] How to calculate the following?

1. ## [SOLVED] How to calculate the following?

a) Prove that the sum of fourth powers of the first n integers is 1/30n(n+1) (2n+1)(3n2+3n+1) .

2. Originally Posted by spmlingam
a) Prove that the sum of fourth powers of the first n integers is 1/30n(n+1) (2n+1)(3n2+3n+1) .

i'm not sure what you are asking, since you don't use parentheses. is it $\frac 1{30n(n + 1)(2n + 1)(3n^2 + 3n + 1)}$?

anyway, i'm thinking induction. did you try that?

3. Hello, spmlingam!

You have a typo . . .

Prove that the sum of fourth powers of the first $n$ integers is:

. . . . . . . . . . . . . . . . . . ${\color{red}\downarrow}$
. . $\frac{n(n+1) (2n+1)(3n^2+3n{\bf{\color{red}-}}1)}{30}$

An inductive proof may be the way to go.
. . [The algebra gets very messy, though.]

Any other approach requires even more algebra . . .