Use mathematical induction to show that `1+3+5+…+ (2n-1) = n^(2)` is true for a numbers n.

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.

Use the principle of mathematical induction to show that a^(n) - b^9n) is divisble by a-b for all natural numbers n.

Use the principle of mathematical induction to show that 5^(2n+1)+3^(n+2).2^(n-1) divisible by 19 for all natural numbers n.

Using the principle of mathematical induction to show that tan^(-1)(n+1)x-tan^(-1)x , forall x in N .

Using mathematical induction prove that n^(2)-n+41 is prime.

Prove the following by the principle of mathematical induction: 1+3+5++(2n-1)=n^(2)idot e, the sum of first n odd natural numbers is n^(2)

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

If A=[111011001] ,then use the principle of mathematical induction to show that A^(n)=[1nn(n+1)/201n001] for every positive integer n.

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all 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