Originally Posted by

**devouredelysium** I have a couple of interrelated questions about series:

Although I've used series for some time, I never really understood what the range of convergence really means. If I have a Taylor series of the function Exp(x) around x=0, does that mean that if I take into consideration only the first 3 terms of the series, it will be very close to the original function around x=0, and that the more terms I take into consideration of the series, the polynomial generated by the series will be getting closer and closer to the real function, both around x=0 and also farer and farer away from that point?