Prove the following by using the principle of mathematical induction for all `n in N`:`1^2+3^2+5^2+dotdotdot+(2n-1)^2=(n(2n-1)(2n+1))/3`

Prove the following by using the principle of mathematical induction for all n in N : (2n+7)<(n+3)^2 .

Prove the following by using the principle of mathematical induction for all n in N : 1 + 2 + 3 + ... + n <1/8(2n+1)^2 .

Prove the following by using the principle of mathematical induction for all n in N : 1/2+1/4+1/8+dotdotdot+1/(2^n)=1-1/(2^n)

Prove the following by using the principle of mathematical induction for all n in N : 1^3+2^3+3^3+""dot""""dot""""dot+n^3=((n(n+1))/2)^2

Prove the following by using the principle of mathematical induction for all n in N : 10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N : a+a r+a r^2+...+a r^(n-1)=(a(r^n-1))/(r-1)

Prove the following by using the principle of mathematical induction for all n in N : 3^(2n+2)-8n-9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n in N : 1^3+2^3+3^3+...........+n^3=((n(n+1))/2)^2

Prove the following by using the principle of mathematical induction for all n in N : 1. 2. 3 + 2. 3. 4 + .. . + n(n + 1) (n + 2)=(n(n+1)(n+2)(n+3))/4

Prove the following by using the principle of mathematical induction for all n in N : (1+1/1)(1+1/2)(1+1/3)...(1+1/n)=(n+1)