1 Answer | Add Yours
First check for `n=1`
So for `n=1` the identity holds. Now assume that the identity holds for all natural numbers greater or equal to `n` i.e.
`1^2+3^2+5^2+cdots+(2k-1)^2=(k(4k^2-1))/3,` `k leq n` (1)
Let's now check for `k=n+1`
Now by using assumption (1) we get
which we were supposed to get. Hence our proof is done.
We’ve answered 317,411 questions. We can answer yours, too.Ask a question