# Homework Help: I have two question about Geometric Progressions

1. Apr 12, 2010

### MrNeWBiE

1. The problem statement, all variables and given/known data

1. Evaluate 4^1/3 . 4^-1/9 . 4^1/27

2. express 0.85555 ..... as a farction . ( hint: write 0.85555= 0.8+0.05(1+0.1+0.01+...))

3. The attempt at a solution

1. well in this question i think the " r " is in the power ,,, and it's -1/3
but how to complete it ,,, what is the story ?
the only think I know is the answer : √(2)

2.can anyone helps me and tell me what is needed in this question ?

Last edited: Apr 13, 2010
2. Apr 13, 2010

### Staff: Mentor

If this is the problem, √2 makes no sense as an answer. Is this the problem exactly as written in your book? This doesn't have anything to do with geometric progression.
Use the hint to find the sum of 1 + .1 + .01 + ... This is a geometric progression with common ratio r = .1. When you get the sum of this progression, multiply by .05 and then add that to .8.

3. Apr 13, 2010

### MrNeWBiE

well this is what in my book
1. Evaluate 4^1/3 . 4^-1/9 . 4^1/27 ........ " i 4get to add the ...... "

i think there is something missing in my book maybe ,,,,

well i will try to solve the 2nd with your method

4. Apr 13, 2010

### Staff: Mentor

For the first one I see now where the geometric progression comes in. Let's look at the partial products.

P1 = 41/3
P2 = 41/3*4-1/9 = 41/3 - 1/9 = ?
P3 = 41/3*4-1/9*41/27 = ?

Fill in where the two question marks are above, and continue finding more partial products, following the pattern that I started.

Hint: ap*aq = ap + q.

5. Apr 13, 2010

### MrNeWBiE

aha,,,
okey thx a lot