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Question: How to get this answer?

Question:How to get this answer?

Budaoy 56 Maple
calculus infinity
July 10 2007
0
Consider a sum: Sum((-1)^(i+1)*Sum(1/j,j=1..i)*x^i,i=1..infinity); value(%); The result given by Maple 11 is: sum((-1)^(i+1)*(Psi(i+1)+gamma)*x^i, i = 1 .. infinity) However, from an calculus book I know the answer is: log(1+x)/(1+x). How can I get this result from Maple? Whether should I give some assumptions? Best wishes.
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