Discover the Sum of a Series: Find the Value with Expert Help

[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}+...

 

[Mark44]

What have you tried?

 

[mathlover1]

What have you tried?

it seems so impossible to do!

 

[Mark44]

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

 

[Susanne217]

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}+...

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 ;)

 

[Dick]

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

 

[gomunkul51]

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).

 

[Mark44]

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).

As given, this series is not an alternating series.

 

[gomunkul51]

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.

 

[Dick]

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.

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