Thread: Determining whether series is convergent or divergent?

1. Determining whether series is convergent or divergent?

Determine whether each series is convergent or divergent

1. (1/2) -(3/8) + (9/32)

2. 1+(3/1 x 2 x3)+ (5/1 x2 x 3 x 4 x 5)

3. (4pi/3)+ 5pi/6 + pi/3

The problem I am having on these is finding the general terms for the series so that I can use the comparison test. Any help would be appreciated as I have been trying to find the An term but these series throw me off.

2. Only three terms for each series?

3. Yes Im only given three terms.

4. I believe you were given the first three terms ... convergence/divergence is checked for infinite series.

$\frac{1}{2} - \frac{3}{8} + \frac{9}{32} - ... = \frac{3^0}{2^1} - \frac{3^1}{2^3} + \frac{3^2}{2^5} - ...$

this infinite series is $\sum_{n=0}^{\infty} \frac{(-3)^n}{2^{2n+1}} = \frac{1}{2}\sum_{n=0}^{\infty} \left(\frac{-3}{4}\right)^n$

... an infinite geometric series with common ratio between -1 and 1.

what does that tell you?

5. 2. 1+(3/1 x 2 x3)+ (5/1 x2 x 3 x 4 x 5)
$1 + \frac{3}{3!} + \frac{5}{5!} + ... + \frac{2n+1}{(2n+1)!} + ... = \sum_{n=0}^{\infty} \frac{1}{(2n)!}$

converge? what test would you use?

6. 3. (4pi/3)+ 5pi/6 + pi/3
$\frac{\pi}{6}\left(8+5+2+ ... \right)$

7. I mean they are infinite series in that they keep going and have those .... at the end.