Prove by mathematical induction that the sum of the squares of first n natural numbers is `1/6n(n+1)(2n+1)`.

Statement - I : The variance of first n even natural numbers is (n^(2) - 1)/(4) Statement - II : The sum of first n natural numbers is (n(n+1))/(2) and the sum of the squares of first n natural numbers is (n(n+1)(2n+1))/(6)

Statement - I : The variance of first n even natural numbers is (n^(2) - 1)/(4) Statement - II : The sum of first n natural numbers is (n(n+1))/(2) and the sum of the squares of first n natural numbers is (n(n+1)(2n+1))/(6)

Prove the following by the principle of mathematical induction: 1+2+3++n=(n(n+1))/(2)ie,the sum o the first n natural numbers is (n(n+1))/(2)

Prove the following by the principle of mathematical induction: 1+2+3++n=(n(n+1))/2idote , the sum o the first n natural numbers is (n(n+1))/2dot

Prove the following by the principle of mathematical induction: 1+3+5++(2n-1)=n^(2)idot e, the sum of first n odd natural numbers is n^(2)

By Mathematical Induction, prove that : n! 1 .

By the principle of mathematical induction prove that the following statement are true for all natural numbers 'n' n (n+1) (n+5) is a multiple of 3.

Prove the following by the principle of mathematical induction: 1+3+5++(2n-1)=n^2i.e. the sum of first n odd natural numbers is n^2dot

Prove by mathematical induction that for every natural number n, 3^(2n+2)-8n-9 is divisible by 8.