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

Explanation

Given,

`1. 2. 3+2. 3. 4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4`

`p(1)=(1(1+1)(1+2)(1+3))/4=6`

which is true.

so,p(k) is true.

let p(k+1) is also true,

`1. 2. 3+2. 3. 4+....+(k+1)((k+1)+1)((k+1)+2)=((k+1)((k+1)+1)((k+1)+2)((k+1)+3))/4`

`=1. 2. 3+2. 3. 4+....+(k+1)(k+2)(k+3)=((k+1)(k+2)(k+3)(k+4))/4`
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