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

(a)Prove that 3^(2n)-1 is divisible by 8.

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

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

Show that x^n-1 is divisible by x-1

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 .

Using principle of mathematical induction prove that n(n+1)(n+5) is a multiple of 3 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.

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

Prove 1.2+2.2^2+3.2^3+………+n.2^n=(n-1)2^(n+1)+2 by using the principle of mathematical induction for all n in N .

Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the principle of mathematical induction for all n in N .