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>> syms A B N
>> symsum(A/(1+A)^N*(B+1/(B+N)),N,1,inf)
ans =
A/(1+A)*(B+1/(B+1))*hypergeom([1, B+1, (B^2+2*B+1)/B],[B+2, (B^2+B+1)/B],1/(1+A))
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