Find the interval of convergence for f(x) = x-(x^2/2)+(x^3/3)-(x^4/4)+.....
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Hello, Originally Posted by jules027 Find the interval of convergence for f(x) = x-(x^2/2)+(x^3/3)-(x^4/4)+..... According to the alternate series test : - should be decreasing - The first one... We want : But has a minimum in 1, when . Hence has to be And this satisfies the second point.
Originally Posted by Moo Hello, According to the alternate series test : - should be decreasing - The second one is always true, whatever x is. Now, the first one... We want : But has a minimum in 1, when . Hence has to be Going off of Moo's work we knwo so far that this is convergent on so we must test the endpoitns....putting int netgative one yields which diverges by either the integral or the p series test inputting 1 we get and since and this converges so the interval of convergence is
Thank you so much guys!
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