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

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

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+1)>2n+1

Prove the following by using the Principle of mathematical induction AA n in N n^(3)+(n+1)^(3)+(n+2)^(3) is a multiple of 9.

Prove the following by using the Principle of mathematical induction AA n in N 3^(2n) when divided by 8 leaves the remainder 1.

Prove the following by using the Principle of mathematical induction AA n in N 2^(3n-1) is divisble by 7.

Prove the following by using the Principle of mathematical induction AA n in N 4^(n) +15n-1 is divisble by 9.

Prove the following by using the Principle of mathematical induction AA n in N Given that 5^(n)-5 is divisble by 4 AA n in N .Prove that 2.7^(n)+3.5^(n)-5 is a multiple of 24.

Prove the following by using the Principle of mathematical induction AA n in N 3.6+6.9+9.12+……+3n(3n+3)=3n(n+1)(n+2)

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