Using the principle of mathematical induction prove that `:` `1. 3+2. 3^2+3. 3^3++n .3^n=((2n+1)3^(n+1)+3)/4^` for all `n in N` .

Using the principle of mathematical induction prove that : the 1.3+2.3^(2)+3.3^(3)++n.3^(n)=((2n-1)3^(n+1)+3)/(4) for all n in N.

Using the principle of mathematical induction,prove that :.2.3+2.3.4+...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4) for all n in N

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Prove the following by using the principle of mathematical induction for all n in Nvdots1.3+2.3^(2)+3.3^(3)+...+n.3^(n)=((2n-1)3^(n+1)+3)/(4)

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

Using the principle of mathematical induction, prove each of the following for all n in N 3^(n) ge 2^(n)

Using the principle of mathematical induction, prove that 1/(1*2)+1/(2*3)+1/(3*4)+…+1/(n(n+1)) = n/((n+1)) .

Using the principle of mathematical induction, prove that (1-1/2)(1-1/3)(1-1/4)...(1-1/(n+1))= 1/((n+1))" for all " n in N .

Using principle of mathematical induction, prove the following 1+3+5+...+(2n-1)=n^(2)

Using the principle of mathematical induction, prove that (7^(n)-3^(n)) is divisible by 4 for all n in N .