Taylor Expansion Of Cot(x)

Posted on 2008-07-11 14:10 By dcasimir ( Maple Rating 3

289)

Categories:

Math Advice (Student)

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,

No

Comment on 2008-07-11 15:24 from alec ( Maple Rating 4

1497)

No, it is not correct. And you can't cancel sum terms in the numerator and the denominator of a fraction.

Alec

Long division

Comment on 2008-07-24 08:57 from edgar ( Maple Rating 2

181)

Use long division of power series. It is like long division of decimals, but no carrying. I hope you are not the victim of "modern" education where you have little idea of the theory behind long division, because it has been deemed "obsolete" due to calculators.
---
G A Edgar

2*4 = 24

Comment on 2008-07-24 13:40 from alec ( Maple Rating 4

1497)

One of my students (a senior) wrote on the test 2*4 = 24, and when I asked him how he got such an aswer, he showed me how he did that using calculator. Obviously, either * button had some problems, or he didn't push it deep enough.

I guess, he could get the same answer in Standard Maple as well. With a possibility of entering such things as 2x without a multiplication sign, why not to enter 24 without it?

Alec

Creative cancellations

Comment on 2008-07-24 13:44 from Doug Meade ( Maple Rating 4

722)

This reminds me that:

sin(x)
------  = sin
   x

Doug

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