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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.
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