f(x)=1/(x^2+3x+2)=1/(x+1)-1/(x+2)=1/(x+1)-(1/2)/(1+x/2)=∑(n=0,+∞)(-x)^n-(1/2)∑(n=0,+∞)(-x/2)^n |x|<1=∑(n=0,+∞)(-1)^n[1-1/2^(n+1)]x^n
