" If "n geqslant4" is an integer,prove by induction that "n^(2)

If nge4 is an integer,prove by induction that n^(2)ltn! .

If nge0 is an integer, prove by induction that 3*5^(2n+1)+2^(3n+1) is divisible by 17.

If nge2 is an integer, prove by induction that, 1+(1)/(4)+(1)/(9)+ . . .+(1)/(n^(2))lt2-(1)/(n) .

If nge3 is an integer, prove by mathmatical induction that, 2n+1lt2^(n) .

If ngt1 is an integer, prove induction that, (1)/(n+1)+(1)/(n+2)+ . . .+(1)/(2n)gt(13)/(24) .

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.

If n is an odd integer, prove that n^(2) is also an odd integer.

If A=[(3,-4),(1,-1)] , prove by induction that A_n=[(1+2n,-4n),(n,1-2n)],n in N

If n is an odd integer, Prove that 16 is a divisor of n^4 + 4n^2 + 11 .

Prove by induction that if n is a positive integer not divisible by 3 , then 3^(2n)+3^(n)+1 is divisible by 13 .