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Question: Limitation in handling telescoping series

Question:Limitation in handling telescoping series

DJJerome1976 535
sum
April 02 2013
1

In trying to obtain the closed form for the nth partial sum for some fairly basic telescoping series. It appears that SumTools[DefiniteSum][Telescoping] works well for rational summands. However, when the same is attempted on summands that are not rational, it fails. Below are a few examples.

 

with(SumTools[DefiniteSum]):

Telescoping(2/(k*(k+3)), k = 1 .. n)

-(2/3)/(n+1)-(2/3)/(n+2)-(2/3)/(n+3)+11/9

 (1)

Telescoping(ln(k/(k+1)), k = 1 .. n)

FAIL

 (2)

Telescoping(2^k/((2^(k+1)-1)*(2^k-1)), k = 1 .. n)

FAIL

 (3)

``

``

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I've tried other commands fromSumTools[DefiniteSum] with no success. The latter two series possess nth partial sums that are easily obtained by hand. Why does Maple appear to have difficulty with them? Is there a better way to approach these problems? For the record, there is no documentation (that I could find) that indicates that Telescoping() is limited to rational summands.

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