Solving the Harmonic Series and Ratio Problem

[Kyousik]

Homework Statement

(infinity)sigma(n=4) [ (2 / n) - (2 / (n -1)) ]

Homework Equations

Harmonic series and ratio?

The Attempt at a Solution

It's supposed to converge to -2/3, but, I don't know how.

The first compare to a harmonic series and we see that goes to 0.

The second, we use a ratio test or something and then compare it? If we simply take the limit it goes to 0.

I don't know how to show it.

 

[Dick]

Write out the first few terms of the series and see if anything occurs to you.

 

[HallsofIvy]

"Telescoping series"