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whats is bigger 1+1 or 1 + half +half of a half + half of a half of a half infinitely

Guest Apr 22, 2015

Best Answer 

 #2
avatar+91001 
+10

These can be quite deceptive MG :)

 

Which is bigger

 1+1=2

 OR

 

$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}....$$

 

This is a Geometric Series,     a=1, r=1/2 = 0.5

 

$$S_\infty=\frac{a}{1-r}=\frac{1}{1-0.5}=\frac{1}{0.5}=2$$

 

So they both have exactly the same value  

Melody  Apr 23, 2015
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5+0 Answers

 #1
avatar+4663 
+10

Let's take this question slow.

 

1+1= 2

 

1+ 0.5 + 2.5 + (half of a half of a half infinitely) (half of infinite is infinite) + infinte = INFINITE 

 

i'm going to the second one

MathsGod1  Apr 22, 2015
 #2
avatar+91001 
+10
Best Answer

These can be quite deceptive MG :)

 

Which is bigger

 1+1=2

 OR

 

$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}....$$

 

This is a Geometric Series,     a=1, r=1/2 = 0.5

 

$$S_\infty=\frac{a}{1-r}=\frac{1}{1-0.5}=\frac{1}{0.5}=2$$

 

So they both have exactly the same value  

Melody  Apr 23, 2015
 #3
avatar+4663 
+5

0.o

 

I don't get it, one has infinity yet it is equivalent to 2?

MathsGod1  Apr 23, 2015
 #4
avatar+78618 
+5

Prove this for yourself MG1  ...   add up the following.......see that the sum is approaching 2 as we add more and more terms.......

1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 +............

See how the series approaches 2 as more terms are added ???

{When you take Calculus later on, this will be one of the main ideas......it's known as a "limit" }

 

  

CPhill  Apr 23, 2015
 #5
avatar+4663 
0

Oh yes!

 

I got the wording wrong!

 

But each time you add those fractions I gets smaller but slowly bigger.

 

PS. I thought he said half of infinity. Not half of a half ... Forever .

MathsGod1  Apr 23, 2015

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