decreasing sequences

**Lupus** · August 5th 2009, 05:52 AM

how do you show that a=n/2^n is a decreasing sequence

**Danny** · August 5th 2009, 06:05 AM

Originally Posted by Lupus

how do you show that a=n/2^n is a decreasing sequence

You need to show that $a_{n} > a_{n+1}$ .

Since $ n > 1 $

then $ 2n > n + 1 $

then $ n > \frac{n+1}{2} $

then $ \frac{n}{2^n} > \frac{1}{2^n} \frac{n+1}{2} = \frac{n+1}{2^{n+1}} $

the desired result.

**Lupus** · August 5th 2009, 06:34 AM

thanks you have been a great help

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