Hello forum! I was wondering if somebody knows of a fancy way of determining the Taylor series expansion of about without computing all the derivatives.

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- January 16th 2013, 08:10 AMMathCrusaderTaylor series arctan(x) without computations
Hello forum! I was wondering if somebody knows of a fancy way of determining the Taylor series expansion of about without computing all the derivatives.

- January 16th 2013, 08:52 AMebainesRe: Taylor series arctan(x) without computations
Determining the series does indeed require computing derivatives, which can appear fairly daunting at first. But after determining the first, second and third derivatives at x=1 you'll see that a simple pattern emerges: arctan(1)= 1/3 + 1/5 - 1/7 +1/9 -....

- January 16th 2013, 08:58 AMBariothRe: Taylor series arctan(x) without computations
none that I can think of sorry!

You should never be afraid of derivating altough! Don't be lazy and get to it! - January 16th 2013, 03:09 PMMathCrusaderRe: Taylor series arctan(x) without computations
Okay thanks!

- January 16th 2013, 05:00 PMTheSaviourRe: Taylor series arctan(x) without computations
It can be derived from geometric series, if that's okay.

- January 16th 2013, 05:08 PMTheSaviourRe: Taylor series arctan(x) without computations
Just noticed that you wanted the expansion at about x = 1. Shouldn't be hard to tweak the above.