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 Nvdots1^(2)+3^(2)+5^(2)+...+(2n-1)^(2)=(n(2n-1)(2n+1))/(3)

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

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

Prove the following by using the Principle of mathematical induction AA n in N 3^(n)>2^(n)

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+3)le(n+3)!

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N

Prove the following by using the principle of mathematical induction for all n in Nvdots1+2+3+...+n<(1)/(8)(2n+1)^(2)

Prove the following by using the principle of mathematical induction for all n in Nvdots1+3+3^(2)+...+3^(n-1)=((3^(n)-1))/(2)

Prove the following by using the principle of mathematical induction for all n in Nvdots1.2+2.2^(2)+3.2^(2)+...+n.2^(n)=(n-1)2^(n+1)+2

Prove the following by using the principle of mathematical induction for all n in Nvdots1.3+2.3^(2)+3.3^(3)+...+n.3^(n)=((2n-1)3^(n+1)+3)/(4)