# Sum of the series help

1. Jun 23, 2010

### mathlover1

Find the value of sum

$$1+\frac{1}{2}-\frac{1}{3}-\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}+...$$

2. Jun 23, 2010

### Staff: Mentor

Re: series

What have you tried?

3. Jun 23, 2010

### mathlover1

Re: series

it seems so impossible to do!

4. Jun 23, 2010

### Staff: Mentor

Re: series

Per the forum rules, you need to show some effort at trying to solve a problem you post.

5. Jun 24, 2010

### Susanne217

Re: series

mathlover,

While I am not allowed to show you how fo find the sum of the series because the old men here would have me booted of the forum but here are a legal hint ;)

Since you have trouble with this I guess you are a first semester student. Look in your Calculus textbook under series and search for the paragraph which deals the series where there is change from plus to minus and back of the series elements ;)

When you have found the right paragragh it will allow you to conclude which kind of series this is then report back :) Because then you will be able to find the sum the very easily ;)

6. Jun 24, 2010

### Dick

Re: series

Try to split the series into two alternating series. Can you sum either one?

7. Jun 25, 2010

### gomunkul51

Re: series

a little warning :)

this series could be summed to any desired value if you change the places of the parts (Riemann's Alternating Series Theorem).

in its natural form you can estimate the sum using Liebnitz Series Theorem (Alternating Series).

Last edited: Jun 25, 2010
8. Jun 25, 2010

### Staff: Mentor

Re: series

As given, this series is not an alternating series.

9. Jun 26, 2010

### gomunkul51

Re: series

May be you right, but:

it is the sum of two alternating series':

sum((-1)^n/2n+1) + sum((-1)^n/2n+2)

and each obeys the rules of an alternating series, and everything I said if valid.

10. Jun 26, 2010

### Dick

Re: series

Sure. And you can EXACTLY sum the original series if you can sum each of those.