- #1

- 18

- 0

**1. The problem:**

Ive been all afternoon struggling with this doubt. Its a bit more teoric than the rest of the exercices i did and i just cant seem to get around it so here it goes :

--------------------------------------------------------------------------------------------------------------------------------

Consider ∑ 1/an a convergent serie of positive terms.

--------------------------------------------------------------------------------------------------------------------------------

What´s the nature of Σ (-1)^n/(an^(2) +1)

## Homework Equations

(Leibniz criterion) ? If ∑(-1)^(n)an is an alternated serie and the sucession(an) is decreasing and his limit→+00 an = 0 then i can say that ∑(-1)^(n)an is converging.

## The Attempt at a Solution

My initial thought was:... a-ha! This is an alternate serie! Because of the (-1)^n ...

So if i prove that the serie 1/an is decreasing since i already know the lim an= 0 i can say that the serie:

(Leibniz criterion)

Σ (-1)^n/(an) IS CONVERGENT however i have two problems...

1- I dont know how to prove that 1/an is decreasing.

2- The serie that they ask me to study is different and even if i could prove that 1/an is decreasing i dont know if through algebric manipulation i could get to:

Σ (-1)^n/(an^(2) +1)

Im not even sure if im going the right way. Anyone has any clue? This is bothering me so much!atement, all variables and given/known data

Last edited by a moderator: