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Prove that 1^2+2^2+dotdotdot+n^2>(n^3)/3...

Prove that `1^2+2^2+dotdotdot+n^2>(n^3)/3,``n in N`

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We will prove it using mathematical induction.
For, `n = 1`,
`L.H.S = 1^2 = 1`
`R.H.S. = 1^3/3 = 1/3`
As, `1 gt 1/3`, our equation is true for `n = 1`.
Let, our equation is true for `n = k` where `k` is a natural number.
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NCERT-PRINCIPLE OF MATHEMATICAL INDUCTION-EXERCISE 4.1
  1. Prove that 1^2+2^2+dotdotdot+n^2>(n^3)/3,n in N

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  2. Prove the following by using the principle of mathematical induction ...

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