(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

[itex]\frac{1}{2^5}[/itex]

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

[itex]\frac{64}{2^{10}}[/itex]

mr magoo

Thanks.

jgens

That should actually be [itex]\frac{64}{2^{11}}[/itex].

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

But that's not a formula.

[tex]\frac{1}{2^n}[/tex] is a formula.

jgens

I could nitpick and argue that [itex]\frac{1}{2^n}[/itex] 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 [itex]\frac{1}{2^5}[/itex]. I really don't understand the objection.

Mentallic

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

[tex]\frac{64}{2^{10}}=\frac{2^5}{2^{10}}[/tex]

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

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:

[tex]\prod_{i=1}^5 \ \frac{1}{2} [/tex]