(iii)Prove that 1+2+3+………+n=`(n(n+1))/2`.by mathematical induction

Consider the statement '' 7^n-3^n is divisible by 4'' Prove the statement using mathematical induction.

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.

Consider the statement p(n):1^3+2^3+3^3+………..+n^3=[(n(n+1))/2]^-2 Prove the statement using mathematical induction.

Consider the statement '' 10^(2n-1)+1 is divisible by 11''. Verify that P(1) is true and prove the statement by using mathematical induction.

(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 .

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

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

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

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