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

Explanation

Given
`P(n):1+1/(1+2)​+1/(1+2+3)​+.....+1/(1+2+3+....n)=(2n)​/(n+1)
`

For n=1, we have

P(1):1, which is true.

Let P(k) be true for some positive integer k i.e,

`1+1/(1+2)​+1/(1+2+3)​+.....+1/(1+2+3+....k)=2k​/
(k+1)`..........(i)

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