Serie Converge/Diverge

1. Feb 21, 2008

oswald

Firs Question

If the serie

∑ Xn = (1/n²)
n=1

converge, then the serie |Xn| converge?

Second question

the serie

∑ X^n / [fat(n)] diverge?
n=1

where fat(n) = n(n-1)(n-2)...4.3.2.1

Its important know the value of X in X^n?

2. Feb 21, 2008

NateTG

3. Feb 21, 2008

Marco_84

1)what is the || of 1/n^2?? think
2) search for geometric series and the hierarchy of infinities..

regards
marco

4. Feb 21, 2008

HallsofIvy

Staff Emeritus
$$\sum_{n=0}^1 \frac{x^n}{n!}$$
is a well known Taylor's series for a simple function and your sum is only slightly different.

5. Feb 21, 2008

oswald

1)

∑ Xn = (1/n²) = 1 + 1/4 + 1/9 ... its a p-serie and converge because p=2>1.
n=1
and

∑ |Xn| = (1/n²) = 1 + 1/4 + ... its the same.. so its converge too.
n=1

2) converge using comparison test, no dought!

6. Feb 21, 2008

Dick

Better to use a ratio test. It will make it easy to see why the value of x doesn't matter.