The Taylor's series for , about x= 0, is . Also so the Taylor's series for is . To get the Taylor's series for multiply that series by :
In order to write that as a single sum, you will want to "adjust" the indices. In the first sum let j= n+ 2 so that n= j- 2 and the sum becomes . For the second, let j= n+ 1 so that n= j- 1 and the sum becomes . In the final sum let j= n so it is the same sum, just indexed by j rather than n.