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Quite an easy question, but I can't do it. I've even tried the tests I knew wouldn't work, (integral test, etc.) and I don't know what to do.

Determine if $\sum\limits_{n=1}^{\infty} \frac{1}{2^n (n+1)}$ converges or diverges.

I suspect it converges but I am not sure. (Not homework, just doing practice questions)

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    $\log_e(4)-1$ if you really want to know2012-03-27

1 Answers 1

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We compare with $\dfrac{1}{2^n}$, the sum of which converges. Since $2^n(n + 1) > 2^n$ for $n \geq 1$, we have $\dfrac{1}{2^n(n + 1)} < \dfrac{1}{2^n}$

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    @t.b.: ....... :-)2012-03-27