(a)Prove the following by using the principle of mathematical induction for all `n in N:2^1+2^2+……..+2^n=2^(n+1)-2`.

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

(b)Prove the following by using the principle of mathematical induction for all n in N:n^2+n is even.

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.

(a)Prove by the principle of mathematical induction that log x^n=nlogx .

(b)Prove by principle of mathematical induction that 2+2^3+2^4+……..+2^n=2(2^n-1)

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 .

Using the principal of Mathematical induction, prove that 1/2+1/4+1/8+…….+1/2^n=1-1/2^n

Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove the statement using the principle of mathematical induction for all natural numbers.

By the Principal of mathematical induction, prove that 1+5+5^2+…..+5^(n-1)=(5^n-1)/4