Your serie is equal to
Now set and we're done.
hi, i have a series 1-1/3+1/5-1/7+..., which i think is also called the Leibniz formula, i know that to find the nth term you can can use (-1)^n/(2n+1), but i need help trying to find a formula or a way to find the sum of the series for a certain number of terms i.e. the sum of the first 10 terms, can anyone help?
Abel's Theorem: If is a power series of radius of convergence of radius such that the series converges at then is continous at .
Here is a more elementary proof.
Proof 2: For any we have . Thus, where depends on the parity of . This tells us that . Thus, . Now . This means, . This means for any if we chose it will mean that is within of . And so, by definition, this series converges to .