4: Since there is no factorial, expansions of the exponential and
trigonometric functions will not help. There is the k as a
multiplicative factor, but unfortunately it is in the numerator, so the
logarithmic expansion is also useless here. Thus the only hope lies with the
geometric expansion.
However, in order to be able to use that the multiplicative factor k
would have to be removed first. We know that it can be cancelled if we
create k also in the denominator, and that can be achieved by
integrating xk−1. However, it is not possible to
create such a power in the series. On the other hand, it is possible to
change k into