Prove that: `1^2+2^2+3^2++n^2>(n^3)/3` for all`""n in Ndot`

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

Prove that: 1+2+3+....+ n<((2n+1)^2)/8 for all ""n in Ndot

Prove that: 1+2+3+n<((2n+1)^(2))/(8) for all n in N.

Prove by Induction, that (2n+7)le (n+3)^2 for all n in N. Using this, prove by induction that : (n+3)^2 le 2^(n+3) for all n in N.

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in Ndot

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in Ndot

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in Ndot

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

Prove that: (1+1/1)(1+1/2)(1+1/3)(1+1/n)=(n+1) for all n in Ndot

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot