Show using mathematical induciton that `n!lt ((n+1)/(2))^n`. Where `n in N and n gt 1`.

Show by using mathematical induction that n^(5) -n is multiple of 5.

Using mathematical induction,prove the following n(n+1)(2n+1),n in N is divisible by 6.

Using the Principle of mathematical induction, show that 11^(n+2)+12^(2n-1), where n is a naturla number is a natural number is divisible by 133.

Let A=[(-1,-4),(1,3)] , prove by Mathematical Induction that A^(n)=[(1-2n,-4n),(n,1+2n)] , where n in N .

Prove that ((n + 1)/(2))^(n) gt n!

Show by mathematical induction that tan^(-1) .(1)/(3) + tan^(-1). (1)/(7) + …+tan^(-1). (1)/(n^2 + n +1)= tan^(-1). (n)/(n+2), AA n inN .

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

Using mathematical induction,prove the following: 1+2+3+...+n<(2n+1)^(2)AA n in N

Let A=[(-1,-4),(1,3)] , by Mathematical Induction prove that : A^(n)[(1-2n,-4n),(n,1+2n)] , where n in N .

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N