Alt Test: Why Does Series 9 Converge?

[foo9008]

Homework Statement

why the author said the series 9 converges by using alternating test ? for the alternating test , the first term the sequence must be in descending order , the it is said to be converges , right?
however , in series 9 , 1 is >(-1/2) , but (-1/2) is not > (1/3)

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

why the author said the series 9 converges by using alternating test ? for the alternating test , the first term the sequence must be in descending order , the it is said to be converges , right?
however , in series 9 , 1 is >(-1/2) , but (-1/2) is not > (1/3)

Homework Equations

The Attempt at a Solution

But 1/2 > 1/3, etc., and that is all that matters. You need to read the material more carefully.

 

[Mark44]

why the author said the series 9 converges by using alternating test ? for the alternating test , the first term the sequence must be in descending order , the it is said to be converges , right?

This makes no sense, "the first term the sequence must be in descending order". For descending order you have to look at the first tem, second term, and so on.

You need to read the conditions that must be met for the alternating series test to be used.