Ok. I know how to the Interval of Convergence of the power series. But when I check for the endpoints. Is it true that if it is centered at 0, 1 end converges and the other diverges. And if it is set at =/ 0 then either both converge or both diverge? If that is not the case isn't there some rule like that to determine?
2007-06-13 13:14:15 · 2 answers · asked by dukebdx12 3 in Science & Mathematics ➔ Mathematics
No, there's no rule. Whenever you are finding the interval of convergence for a power series, you have to simply plug the endpoint values into the series and simplify, then decide whether that simplified series converges using any suitable test.
2007-06-13 14:00:55 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
partly a), the radius of convergence is |r| < a million. This situation is a lengthy way a lot a lot less complicated than what you've been attempting. because you comprehend that ln(a million+x)=x-x^2/2 + x^3/3 + .... in ordinary words replace x^2 in for x contained contained in the above formula to get ln(a million+(x^2)) = x^2 + x^4/2 + x^6/3...(-a million)^(n+a million)*x^2n/n+....
2016-11-23 19:06:46 · answer #2 · answered by ? 4 · 0⤊ 0⤋