If `n in NN` ,the prove by mathematical that `1+3+5+….+(2n-1)=n^(2)`

If n in N,then prove by mathematical induction that 7^(2n)+2^3(n-1).3^(n-1) is always a multipe of 25.

For all ninNN , prove by principle of mathematical induction that, 1+3+5+ . . .+(2n-1)=n^(2) .

For all ninNN , prove by principle of mathematical induction that, 1^(2)+3^(2)+5^(2)+ . . .+(2n-1)^(2)=(n)/(3)(4n^(2)-1) .

For all ninNN , prove by principle of mathematical induction that, (1)/(1*2)+(1)/(2*3)+(1)/(3*4)+ . . .+(1)/(n(n+1))=(n)/(n+1) .

For all ninNN , prove by principle of mathematical induction that, (1)/(2)+(1)/(4)+(1)/(8)+ . . .+(1)/(2^(n))=1-(1)/(2^(n)) .

For all ninNN , prove by principle of mathematical induction that, 1+(1)/(1+2)+(1)/(1+2+3)+ . . .+(1)/(1+2+3+ . . .+n)=(2n)/(n+1) .

For all ninNN , prove by principle of mathematical induction that, 2^(2)+5^(2)+8^(2)+ . . . to n terms =(n)/(2)(6n^(2)+3n-1) .

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

For all ninNN , prove by principle of mathematical induction that, 2*7^(n)+3*5^(n)-5 is divisible by 24.

For all ninNN , prove by principle of mathematical induction that, 1*1!+2*2!+3*3!+ . . .+n*n ! =(n+1)!-1 .