How to find the minimum of n for which #((2^n)-1)lna/(2^(n-1)n) < 0.01lna# ?

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Answer 1 · 2017-12-06T10:41:18

#n ge 200#

#((2^n-1)lna)/(2^(n-1)*n) < 0.01*lna#

Assuming #lna > 1# we have

#2^n-1 < 0.01/2 2^n n# or

#2^n(1-n/200 ) < 1 rArr n ge 200#

How to find the minimum of n for which #((2^n)-1)lna/(2^(n-1)*n) < 0.01*lna# ?