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Which is greater 70^71 or 71^70?

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Which is greater 70^71 or 71^70?
posted Aug 16, 2015 by anonymous

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2 Answers

+1 vote

70^71 is greater than 71^70

answer Aug 17, 2015 by Kewal Singh Paneser
Yes correct I also got the same,
actually for all a > 2; a^(a+1) > (a+1)^a

+1 from me
0 votes

70^71 is greater than 71^70, here is the explanation:


Let's assume 71^70 is greater than 70^71 , if this is a case than (71^70 / 70^71) must be greater than or equal to 1.
One can write expression as: (70+1)^70 / (70^70 * 70) ,here 70^70 * 70 =70^71
= ((70 + 1 / 70) ^ 70) * 1 / 70)
=((1+1/70)^70 *(1/70)
now 1/70 =0.014 approximately and the only way it could be greater that 1 is to multiply is by 100.
(1+1/70)^70 can't be 100. Hence our assumption is wrong and 70^71 is greater than 71^70.

answer Jun 10, 2016 by Shahsikant Dwivedi
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