Using principle of mathematical induction prove that `n(n+1)(n+5)` is a multiple of 3 for all `n in N`.

Using mathematical induction prove that 41^n-14^n is a multiple of 27 for all n in N

Using mathematical induction prove that 10^(2n-1)+1 is divisible by 11 for all n in N

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

Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1) Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n .

Consider the statement P(n):1+3+3^2+...+3^(n-1)=(3^n-1)/2 .Prove by principle of mathematical induction,that P(n) is true for all n inN

Using the principle of Mathematical induction,prove that 10^(2n-1)+1 is divisible by 11.

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Using the principal of Mathematical induction verify that P(n) is true for all natural numbers.

Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in N

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

(b)Prove by the principle of mathematical induction that 3^n>2^n.