Prove the following by the principle of mathematical induction: `\ 1. 2+2. 2^2+3. 2^3++n .2^n=(n-1)2^(n+1)+2`

Explanation

Given,

P(n):`1.2+2.2^2++3.2^3+⋯………………..+n.2^n=(n-1)* 2^(n+1)+2`

Putting n = 1

LHS = 2

RHS = 2

So,P(n) is true for n=1

lets assume p(n) is true for n=k

`1.2+2.2^2+3.2^3+...........+k.2^ k`

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