The goal is to show how many terms of the series 1/n*2^n are needed to approximate ln 2 with 6 digit accuracy.

So I set

1/(2^(n+1)*(n+1)<10^-6

And now this means

2^n*(n+1)>500,000

I know the answer is supposed to be 17, but the brain fade is in solving this inequality (unless I'm doing the whole problem wrong). I know it should be easy, but I'm at a little loss here.

Thanks.