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` .

Explanation

Given
P(n)=`1.3+(2.3)^2+(3.3)^3+.....+(n.3)^n=((2n−1)*3^(n+1)+3)/4​`

Let n=1,
P(1)
=RHS=L.H.S=3

P(n) is true for n=1

Assume P(k) is true,

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