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 x^k−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 2k and then remove it by integrating x^2k−1, which is something that we can create there. We see that the procedure will involve integration, which is usually handled more easily if you first denote the sum of the given series as f (x) and then manipulate simultaneously both sides of this equality.

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