I have no clue how to do this, can someone please help?? :(
Does the series $$\large \sum_{n=1}^{\infty} \frac{2^{n}}{n+1}$$, converge or diverge? And state which tests shows this.

Question

I have no clue how to do this, can someone please help?? :(
Does the series $$\large \sum_{n=1}^{\infty} \frac{2^{n}}{n+1}$$, converge or diverge? And state which tests shows this.

anonymous · Answer

It diverges, since derivative of  2^n/(n+1) will always above 1

anonymous · Answer

so what is the steps to find that?
Do we derive it?

anonymous · Answer

Try limit test

anonymous · Answer

and which test do we use for it? :) my question asks to state which test? e.g. nth term test, integral, geometric

anonymous · Answer

oh which is the limit test? I haven't come across it

anonymous · Answer

Try nth term test.

anonymous · Answer

I think I am making mistakes in the test, do you know how to use the test?

anonymous · Answer

The nthe term test state that if none of the series term is 0, the the series must diverges. Now try to find a term that is equal to 0, if not then the series must diverges

anonymous · Answer

I read that bit :) how do I go about proving that with the formula $$\large \lim_{n =0 } a_{n} \neq 0$$

anonymous · Answer

It's lim n=infinite, not 0
And use l'hospital rule.

anonymous · Answer

l'hospital rule? :S I can't find that rule anywhere in my notes I took down or are reading
do you mean D'Alembert's rule?