(1.0 / 2) process repeated 5 times; what is the algrabraic formula?

[mr magoo]

1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.0625
0.0625 / 2 = 0.03125

What is the algebraic formula for this?

 

[jgens]

$\frac{1}{2^5}$

 

[mr magoo]

This is a new one;

64 / 2 = 32
32 / 2 = 16
16 / 2 = 8
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1
1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.0625
0.0625 / 2 = 0.03125

$\frac{64}{2^{10}}$

 

[mr magoo]

Thanks.

 

[jgens]

That should actually be $\frac{64}{2^{11}}$.

Edit: Enclose your "10" in { } to make it appear correctly.

 

[mr magoo]

Your right, I added one too many and thought there was only ten.

 

[mr magoo]

Thanks for the editing tip.

 

[Char. Limit]

$\frac{1}{2^5}$

But that's not a formula.

$$\frac{1}{2^n}$$ is a formula.

 

[jgens]

But that's not a formula.

I could nitpick and argue that $\frac{1}{2^n}$ is actually an expression and not a formula since it does not contain an equals sign; but the distinction is really not all that relevant. The OP wanted to know how to express "1 divided by 2 fives times" algebraically and one way is $\frac{1}{2^5}$. I really don't understand the objection.

 

[Mentallic]

This is a new one;

64 / 2 = 32
32 / 2 = 16
16 / 2 = 8
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1
1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.0625
0.0625 / 2 = 0.03125

$\frac{64}{2^{10}}$

Also notice that since we divided 64 by 2 five times and we got to 1, so $\frac{64}{2^5}=1$ rearranging, we get $64=2^5$ so we can express the answer as

$$\frac{64}{2^{10}}=\frac{2^5}{2^{10}}$$

And if you remember the rule of indices, $$\frac{2^a}{2^b}=2^{a-b}$$ so $$\frac{2^5}{2^{10}}=2^{5-10}=2^{-5}=\frac{1}{2^5}$$

As we got in your first question.

 

[rcgldr]

The formula (not sure if this is considered algebraic) or notation for a product series in the original example would be:

$$\prod_{i=1}^5 \ \frac{1}{2}$$