# 3 true or false

1. Apr 23, 2006

### Spruance

True or false, justify your answer

1) If $$\sum_{n=1}^\infty a_n$$ converges, then $$\sum_{n=1}^\infty (-1)^n \ a_n$$ converges.

2) If $$\sum_{n=1}^\infty a_n$$ converges and $$\sum_{n=1}^\infty (-1)^n \ a_n$$ converges, then $$\sum_{n=1}^\infty a_n$$ converges absolutely.

3) If $$\sum_{n=1}^\infty a_n$$ converges absolutely, then $$\sum_{n=1}^\infty (-1)^n \ a_n$$ converges absolutely.

Can anybody help me with this one?

Thanks in advance

Last edited: Apr 23, 2006
2. Apr 23, 2006

### Hootenanny

Staff Emeritus
your [t e x] tags must be in lower case.

~H

3. Apr 23, 2006

### Spruance

Thank you, Hootenanny. That fixed everything!

4. Apr 23, 2006

### Hootenanny

Staff Emeritus
RE: Your question, what are the criteria for absolute convergence?

~H

5. Apr 23, 2006

### HallsofIvy

Staff Emeritus
Or, what is the definition of "absolute convergence"?

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