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let
n/[(n+1)(n+2)] ≡ A/(n+1) +B/(n+2)
=>
n≡ A(n+2) +B(n+1)
n=-1, => A=-1
n=-2, =>B=2
ie
n/[(n+1)(n+2)] ≡ -1/(n+1) +2/(n+2)
//
n.2^n/[(n+1)(n+2)]
=2^n .{ n/[(n+1)(n+2)] }
=2^n .[-1/(n+1) +2/(n+2) ]
=[-2^n/(n+1) + 2^(n+1)/(n+2) ]
n/[(n+1)(n+2)] ≡ A/(n+1) +B/(n+2)
=>
n≡ A(n+2) +B(n+1)
n=-1, => A=-1
n=-2, =>B=2
ie
n/[(n+1)(n+2)] ≡ -1/(n+1) +2/(n+2)
//
n.2^n/[(n+1)(n+2)]
=2^n .{ n/[(n+1)(n+2)] }
=2^n .[-1/(n+1) +2/(n+2) ]
=[-2^n/(n+1) + 2^(n+1)/(n+2) ]
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