what is the series of xcosx

Question

anonymous · Answer

what is maclaurin series for xcosx

anonymous · Answer

Are you allowed to start from the maclaurin serie of cosx?

anonymous · Answer

yes

vishal_kothari · Answer

http://mathinsite.bmth.ac.uk/pdf/macseries_theory.pdf

anonymous · Answer

Ok, well the maclaurin serie of cosx is:

$$1 - x ^{2}/2! +  x ^{4}/4!  - x ^{6}/6! + ...$$

You multiply it by x, which gives:

$$x - x ^{3}/2! +  x ^{5}/4!  - x ^{7}/6! + ...$$

anonymous · Answer

Which is equal to $$\sum_{n=0}^{\infty} x ^{2n+1} / (2n)!$$

anonymous · Answer

$$\sum_{1}^{\infty}(-1)^n/(2n+1)*x^n+1$$

anonymous · Answer

oh damn my bad, I forgot the alternating (-1)^n you're right

anonymous · Answer

so this is the general foemula for coscx

anonymous · Answer

no cosx

anonymous · Answer

Your summation form is wrong however. I wrote the right one but I'm missing (-1)^n

anonymous · Answer

oh ok

anonymous · Answer

$$\sum_{0}^{\infty}(-1)^n*2^(n+1)/5^n$$

anonymous · Answer

No. All you have to do is write down a few terms of the normal cosx serie expansion, then multiply them all by x. You can confirm my answer here: http://www.wolframalpha.com/input/?i=xcos%28x%29+

anonymous · Answer

You'll have to scroll down to the "Series expansion at x=0" part

anonymous · Answer

Also as I said earlier, I forgot the (-1)^n term (re-typing the equation takes too long :P)