First of all if i have a function with all negative terms is it possible to determine its convergence simply by factoring the negative one, treating the other terms as a positive series determine its convergence then assume that multiplying by the constant negative one will not change its convergence.(adsbygoogle = window.adsbygoogle || []).push({});

Second, one cannot say the taylor series is equal to the function whose taylor series has been determined unless one states explicitly the radius of convergence, true? Can one use the ratio test to determine the interval of convergence or does one have to use the remainder, i.e. Lagrange form or another, and see if it goes to zero as n goes to infinity to determine convergence:

[tex]R_n(x) = \frac{f^{(n+1)}(\xi)}{(n+1)!} (x-a)^{n+1}.[/tex]

thanks

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# Simple questions regarding Taylor series

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