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Question: How to calculate the left-hand limit?

Question:How to calculate the left-hand limit?

Alfred_F 280 Maple
limit summation
March 09 2025
2

For practice, I would like to calculate the left-hand limit according to the attached file. The computer does not finish. The result pi^2/6 is known from a calculation "on foot".

restart

``

limit((1-t)^2*(sum(k*t^k/(1-t^k), k = 1 .. infinity)), t = 1, left)

limit((1-t)^2*(sum(k*t^k/(1-t^k), k = 1 .. infinity)), t = 1, left)

 (1)

"(->)"``

``

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