lets first take function p(n) as p(2) where our n=2 i=1,2 taking real values

then 1/1(1+1)+1/2(2+2)=2/(2+1)

hence 1/2+1/6=2/3

where denominator 3=n+1 ,,,,n=2

so sum p(n)=n/(n+2)

that is the correct method by induction, just take real values and factorise

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