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- Thread starter mertcan
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Ssnow

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Hi, where is your attachment? ...

- #3

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ohh I really apologise....... I upload it here, and looking forward to your response

Also let me express my question again: If you look at my attachment you can see that the book express that for the situation of x=+,-(1/L) we need further investigation. It means being converged or diverged is not precise. I would like to ask: Is there remarkable proof that if x=+,-(1/L) convergence or divergence is not precise??? Could you provide me with that proof??? I really really wonder it....Thanks in advance....

Also let me express my question again: If you look at my attachment you can see that the book express that for the situation of x=+,-(1/L) we need further investigation. It means being converged or diverged is not precise. I would like to ask: Is there remarkable proof that if x=+,-(1/L) convergence or divergence is not precise??? Could you provide me with that proof??? I really really wonder it....Thanks in advance....

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Ssnow

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Actually, I am aware that comparison between terms in the sum as ##a_{n+1}x^{n+1}## and ##a_{n}x^{n}## have the same behavior for ##n\rightarrow \infty## but my main question is : Why can't we decide whether it converges or not??? Is there mathematical proof???

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You say that ratio test can not tell us whether or not it converges??? I am confusing Could you spell it out giving some Mathematical Stuff, proofs derivations ?????_{i}, there are too many different cases that will give the same L. Some converge and others do not. You can make examples that do anything you want just by manipulating the signs of the coefficients, a_{i}.

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FactChecker

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I mean that only for the case of x = +-L. It works otherwise.You say that ratio test can not tell us whether or not it converges??? I am confusing Could you spell it out giving some Mathematical Stuff, proofs derivations ?????

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Ok I got it if ratio is 1 the your example is satisfying, but I am also curious about the Mathematical proof of it , I need some proof to convince myself. Could you give some proof that at critics point we do not know convergence or divergence besides the examples??????I mean that only for the case of x = +-L. It works otherwise.

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There is a proof that it will converge if |x| < L and a proof that it will not converge if |x| > L. There are only counterexamples for the case |x| = L. The counterexamples prove that the proof does not work in that case.Ok I got it if ratio is 1 the your example is satisfying, but I am also curious about the Mathematical proof of it , I need some proof to convince myself. Could you give some proof that at critics point we do not know convergence or divergence besides the examples??????

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