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 Nvdots(2n+7)<(n+3)^(2)

Prove the following by using the principle of mathematical induction for all n in Nvdotsx^(2n)-y^(2n) is divisible by x+y

Prove the following by using the principle of mathematical induction for all n in Nvdots10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in Nvdotsn(n+1)(n+5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in Nvdots41^(n)-14^(n) is a multiple of 27

Prove the following by using the principle of mathematical induction for all n in Nvdots3^(2n+2)-8n-9 is divisible by 8.

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 for all n in Nvdots(1)/(2)+(1)/(4)+(1)/(8)+...+(1)/(2^(n))=1-(1)/(2^(n))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1+(3)/(1))(1+(5)/(4))(1+(7)/(9))...(1+((2n+1))/(n^(2)))=(n+1)^(2)

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