Determine whether the series converges, and if it converges, determine its value.

**ewkimchi** · May 18th 2010, 11:09 PM

Consider the series

Determine whether the series converges, and if it converges, determine its value.

I know it converges, I got 7/10, but it's wrong. Please help! =)

**Prove It** · May 18th 2010, 11:31 PM

Originally Posted by ewkimchi

Consider the series

Determine whether the series converges, and if it converges, determine its value.

I know it converges, I got 7/10, but it's wrong. Please help! =)

$\sum_{n =1}^{\infty}\frac{(-7)^{n- 1}}{10^n} = \frac{1}{10} - \frac{7}{100} + \frac{49}{1000} - \frac{343}{10\,000} + \dots - \dots$ .

This is a geometric series with $a = \frac{1}{10}$ and $r = -\frac{7}{10}$ .

Since $|r| < 1$ , the series is convergent, and

$S_{\infty} = \frac{a}{1 - r}$

$= \frac{\frac{1}{10}}{1 - \left(-\frac{7}{10}\right)}$

$= \frac{\frac{1}{10}}{\frac{17}{10}}$

$= \frac{1}{17}$ .

Thread: Determine whether the series converges, and if it converges, determine its value.

LinkBack

Thread Tools

Display

Determine whether the series converges, and if it converges, determine its value.

Similar Math Help Forum Discussions

[SOLVED] Use any method to determine if series converges

[SOLVED] Determine whether series converges or diverges

[SOLVED] Determine if the series converges

determine of series converges or diverges

How do I determine if the series converges?

Search Tags