Find the sum of the following series:
I don't know where to begin in this, can't recognize any of the known series.
Which is the general term of the series where and
So the sum
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Consider the series
Now integrate to get
Note that this is your series when
Other solution ( using D for derivative and arctgh(x) for ArcTanh(x) )
we know that and so
using the geometric series for we have
So the sum would be when ? to three s.f.
by the parcial fraction decomposition
Originally Posted by arze
General term: (Correct.)
Which is the general term of the series where (Should be n = –1.) and
So the sum (Make that .)
Answer is: ..
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