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 to show that the given series diverges. However, note that
if we ignore the k! for a second, then we get a geometric series with
There is a little problem, though, that the series for exponential starts
with