# Help with sequence formula

• March 6th 2013, 10:35 AM
amyw
Help with sequence formula
I have the sequence: <1, 3/2, 7/4, 15/8, 31/16, 63/32,...> and I need to find a formula to describe it. Can anyone help? I must have missed the day when this was taught.
• March 6th 2013, 07:21 PM
TheEmptySet
Re: Help with sequence formula
Quote:

Originally Posted by amyw
I have the sequence: <1, 3/2, 7/4, 15/8, 31/16, 63/32,...> and I need to find a formula to describe it. Can anyone help? I must have missed the day when this was taught.

The numerator can be defined recursively. Let

Here is a hint: the number is the sum of the geometric series $2^n$

$2^{0}=1 \\ 2^{0}+2^1=3 \\ 2^{0}+2^1+2^2=7 \\ 2^{0}+2^1+2^2+2^3=15$

So what does

$\sum_{k=0}^{n}2^k=$?