# Homework Help: Infinite Series

1. Feb 23, 2005

### a_ng116

If you have a repeating decimal such as 0.45454545.... and the question was asking for it to be expressed as an infinite series and find the sum of the series, would it be correct to approach it like this:

$$0.45454545... = \frac {45}{100}+ \frac{45}{10000} + \frac{45}{1000000}....$$

so $$a=\frac{45}{100}$$ and $$r=\frac {1}{100} or 0.01$$

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

i get: $$= \frac {45/100} {1-0.01} = \frac {5}{11}$$

I think this is right but I'm not sure....any thoughts? Please and thank you.

2. Feb 23, 2005

### NateTG

Works for me.

You can check your answer by, for example, doing the division to see what comes up.

3. Feb 23, 2005

### Diane_

Your answer is certainly right. Remember the Algebra I approach to this problem:

x = .45...

100x = 45.45...

100x - x = 45.45... - .45...

99x = 45

x = 45/99 = 5/11

4. Feb 23, 2005

### a_ng116

Thanks for the help guys, I really appreciate it.