# Thread: How many terms in a geometric series

1. ## How many terms in a geometric series

How many terms of the geometric sequence 1.6, -.8, .4, -.2.... must be added together starting with the first term and adding in order, so that the sum is within .001 of 16/15. So the Sum must be larger than 16/15 - .001 but smaller than 16/15 + .001. Use Algebra

2. Originally Posted by stones44
How many terms of the geometric sequence 1.6, -.8, .4, -.2.... must be added together starting with the first term and adding in order, so that the sum is within .001 of 16/15. So the Sum must be larger than 16/15 - .001 but smaller than 16/15 + .001. Use Algebra
The error in an alternating geometric series is less than the last term added

so we need $\displaystyle \frac{1.6}{2^n}=.001$

Solving for n gives $\displaystyle n \approx 10.64$

so we will need to add at least 11 terms.

3. i dont see how you got that equation

im just generally confused on what you are saying

4. Originally Posted by stones44
i dont see how you got that equation

im just generally confused on what you are saying

$\displaystyle \sum_{n=0}^{\infty}\underbrace{1.6\left( \frac{-1}{2}\right)^n}_{a_n}=1.6-0.8+0.4-0.2+...$
Setting $\displaystyle a_n=\mbox{error}$ and solve for n as above