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Prove by the principle of mathematical i...

Prove by the principle of mathematical induction that for all `n in N :` `1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)`

Text Solution

Verified by Experts

Given,
P(n)=`1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)`
For n=1
=`1^2=1`
P(n) is true
P(k):
`1^2+2^2+3^2+........+k^2=(k(k+1)(2k+1)​)/6`
...
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