prove-that-a-r-1-r-1-

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 \dots q u e s t i o n

n o t c l e a r \dots

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!} + \dots - 1}{r}

= \lim_{r \to 0} \frac{r + \frac{r^{2}}{2!} + \dots}{r} = \lim_{r \to 0} (1 + \frac{r}{2!} + \dots) = 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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