Find-all-the-solution-that-fulfilled-the-equation-below-1-1-x-x-1-1-1-2013-2013-

Question Number 10856 by Joel576 last updated on 27/Feb/17

Find all the solution that fulfilled the equation below

{(1 + \frac{1}{x})}^{x + 1} = {(1 + \frac{1}{2013})}^{2013}

Answered by DrDaveR last updated on 12/Mar/17

J u s t - 2014 . T h e r e c a n b e n o p o s i t v e s o l u t i o n . T h e f u n c t i o n i s

m o n o t i n i c a l l y d e c r e a s i n g s o t h e r e c o u l d b e o n e n e g a t i v e

s o l u t i o n . A s (1 + 1 / x) = 1 / (1 - 1 / (x + 1)) t h e n t h e R H S c a n b e

w r i t t e n {(1 - 1 / 2014)}^{- 2013} w h i c h g i v e s t h e s o l u t i o n .

Facebook Tweet Pin