How do I show that the series diverges. The question asks to us to use Maclaurin series to compare the series with some other series.
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Originally Posted by mohammadfawaz The question asks to us to use Maclaurin series to compare the series with some other series. So how did it work for you? I guess you wrote and expanded the exponent first, up to some order, etc...
What I actually did is to use the binomial theorem.
We get an inequality for : .
Expanding e, and taking the difference, I got:
But I'm stuck there. I don't know if I'm on the right track.
Originally Posted by mohammadfawaz Good idea, but the right hand side will give you a convergent series, hence you get nothing. (Greater than a convergent series proves nothing)
What you could do is use for in the expansion I wrote. Or the asymptotic expansion as .
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