sinx-x-b-n-0-1-n-2n-1-x-2n-1-x-b-prove-that-

Question Number 186941 by mathlove last updated on 12/Feb/23

\frac{s i n x}{x^{b}} = \frac{\underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{(2 n + 1)!} x^{2 n + 1}}{x^{b}}

p r o v e t h a t

Commented by mr W last updated on 12/Feb/23

x^{b} = x^{b} n e e d s n o p r o o f .

\sin x = \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n + 1}}{(2 n + 1)!}

j u s t a p p l y t a y l o r s e r i e s f o r f u n c t i o n

f (x) = \sin x a t p o i n t x = 0 .

\Rightarrow s e e t a y l o r s e r i e s!

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