Seq Convergence: Does a_n = (-1)^(n+1)/(2n-1) Converge or Diverge?

[whatlifeforme]

Homework Statement

Converge or diverge?

Homework Equations

\displaystyle a_{n} = \frac{(-1)^{n+1}}{2n-1}

The Attempt at a Solution

all i know is to perhaps take ln of numerator and denominator to get the exponent down below?

 

[SammyS]

Homework Statement

Converge or diverge?

Homework Equations

\displaystyle a_{n} = \frac{(-1)^{n+1}}{2n-1}

The Attempt at a Solution

all i know is to perhaps take ln of numerator and denominator to get the exponent down below?

Do you know the squeeze theorem ?

 

[whatlifeforme]

Do you know the squeeze theorem ?

I do.

 

[STEMucator]

I do.

It appears the sequence is conditionally convergent.

1. What is $\sum |a_n| = \space ?$

2. Is $a_n > a_{n+1}$? For sufficiently large n.

3. lim n→∞ ... = ...

 

[LCKurtz]

Homework Statement

Converge or diverge?

Homework Equations

\displaystyle a_{n} = \frac{(-1)^{n+1}}{2n-1}

The Attempt at a Solution

all i know is to perhaps take ln of numerator and denominator to get the exponent down below?

Are you asking about a sequence or a series? You should fill in part one of the homework template more completely.

 

[whatlifeforme]

sequence.

 

[LCKurtz]

So show us what you have done so far in thinking about whether that sequence has a limit.