Question: Taylor Expansion Of Cot(x)

A problem instructed me to construct a Taylor/Maclaurin series for cot(x) by dividing cos(x) by sin(x).

I did this quotient by putting both summations over each other then cancelling common terms.

I've always had some difficulties with summation, or the rules of the summation symbol and would like to know if that operation was legal.

In this case both summations began from the same starting point for the dummy variable, n.

Whenever this is the case is it correct to say that the quotient of two sums is the sum of the quotient?

very respectfully,



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