Prove that :`1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6`

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

Prove that: 1^2+2^2+3^2.....+n^2>(n^3)/3, n in N

Prove that : 1^3+2^3+3^3++n^3={(n(n+1))/2}^2dot

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))

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)

Using the principle of mathematical induction, prove that : 1. 2. 3+2. 3. 4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4^ for all n in N .

Using the principle of mathematical induction prove that : 1. 3+2. 3^2+3. 3^3++n .3^n=((2n-1)3^(n+1)+3)/4^ for all n in N .

Prove that : 1+2+3++n=(n(n+1))/2

For all n geq1 , prove that 1^2+2^2+3^2+4^2+dotdotdot+n^2= (n(n+1)(2n+1))/6

Prove that: \ ^(2n)C_n=(2^n[1. 3. 5 (2n-1)])/(n !)