Re: Does this series converge (1 - (log n)/n)^n

Quote:

Originally Posted by

**buckeye1973** Hmm.. How about this..

Take as a given that

is an increasing sequence with

. (It is true:

see here.)

For

we know that

but that same sum diverges for any other r.

Let

. Then, by definition of limit, there exists

such that for each

,

. Thus for any

, there are an infinite number of terms such that

. Hence,

is greater than any (monic) convergent geometric series, and is therefore divergent.

QED?

Anyone? I'm afraid that this post has had so many replies that nobody wants to read it, but I haven't got a usable answer. Plato gave a good hint maybe, but I don't follow it..