Problem: Find the sum of the series
Solution: This series contains parts of the form ck, but there are more of them, so first we should tidy up the given expression.
This is not a geometric series because of that k in the
denominator, so there is no way to sum it up using the geometric approach, and
there also seems no way to change it into a difference in order to apply the
telescopic series trick. So there are two possibilities. Either we will be
able to use the
power series approach, or we show
that the given series diverges. However, note that if we ignore the k
for a second, then we get a geometric series with
Since the given series can be made to fit this power series, we can use this expansion to sum up the given series.
