prove that. ((a^r −1)/r)=1


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Question Number 49817 by Aditya789 last updated on 11/Dec/18

$prove that . \frac{a^{r} - 1}{r} = 1$
Commented by tanmay.chaudhury50@gmail.com last updated on 11/Dec/18

$w h a t i s t h e r e l a t i o n b e t w e e n a a n d r . . . q u e s t i o n$ $n o t c l e a r . . .$
	Answered by $@ty@m last updated on 11/Dec/18

	$P l . c h e c k t h e q u e s t i o n .$ $I n m y o p i n i o n, i t s h o u l d b e :$ $P r o v e t h a t \lim_{r \to 0} \frac{e^{r} - 1}{r} = 1$ $P r o o f :$ $\lim_{r \to 0} \frac{e^{r} - 1}{r} = \lim_{r \to 0} \frac{1 + r + \frac{r^{2}}{2!} + . . . - 1}{r}$ $= \lim_{r \to 0} \frac{r + \frac{r^{2}}{2!} + . . .}{r} = \lim_{r \to 0} (1 + \frac{r}{2!} + . . .) = 1$
	Commented by $@ty@m last updated on 11/Dec/18

	$S i m i l a r l y, i t c a n b e s h o w n t h a t :$ $\lim_{r \to 0} \frac{a^{r} - 1}{r} = \ln a$
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