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

(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 .

(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 .

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

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

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

Prove by using the principal of Mathematical Induction P(n)=1+3+3^2+…..+3^(n-1)=(3^n-1)/2 is true 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 .

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

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