Using division of power series to find the first 3 nonzero terms

[gummybears123]

1. Use multiplication or division of power series to find the first 3 nonzero terms in the Maclaurin series of the function x/sinx.



2. the maclaurin series for sinx is $$\sum(-1)^{n}x^{2n+1}/(2n+1)!$$



3. I've tried to divide x/sinx substituting sinx for the maclaurin series but I seem to get stuck. Any help is much appreciated!

 

[Dick]

You are probably making too much of a big deal over this.
sin(x)=x-x^3/6+x^5/120-... Just do polynomial long division of that into x. You can just keep the first three terms. Stop after you get three terms in the quotient.