I have two question about Geometric Progressions

[MrNeWBiE]

Homework Statement

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+...))

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 ?

 

[Mark44]

Homework Statement

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

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.

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

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 ?

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.

 

[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

 

[Mark44]

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

P₁ = 4^1/3
P₂ = 4^1/3*4^-1/9 = 4^{1/3 - 1/9} = ?
P₃ = 4^1/3*4^-1/9*4^1/27 = ?

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

Hint: a^p*a^q = a^{p + q}.

 

[MrNeWBiE]

aha,,,
okey thanks a lot