find the taylor series of a function of two variables
I was given this practice question...
Find the Taylor Series for f(x,y)=1/(2+xy2).
I though this would be easy but I can't figure out how they got the answer that they did in the back of the book.
I tried to find the pattern by finding f1 and f2, then f11, f12 and f22. Then I put it into the form of a taylor polynomial to find the pattern.
After this point I ended up with 1/2 + (3xy2)/4 + (5x2y4 - 4xy2)/8 ...
The answer in the back of the book is: Sum n=0 ->inf (-1)n xny2n/2(n+1)
I understand the (-1)n and the 2(n+1) and for the most part I can see the xny2n part also but something is off somewhere.
If anyone can give me any feed back I would really appreciate it.