• anonymous
If a serie is convergent does it mean the serie can be rewritten as a taylor polynomial but it can't be rewritten if it's divergent? If not what's the meaning of convergence I don't think I get the textbook approch?
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • katieb
I got my questions answered at in under 10 minutes. Go to now for free help!
  • mathmate
If the series is given by \( S=\sum_{i=1}^\infty a_i \), and the partial sum to n terms defined by \(S_n = \sum_{i=1}^n a_i \), then S is said to be convergent if for any \(\epsilon >0\) N can be found such that \( |S_k-S_N|<\epsilon\) \( \forall k>N \). A Taylor polynomial is a Taylor's series truncated after the first n terms, where \(n<\infty \).

Looking for something else?

Not the answer you are looking for? Search for more explanations.