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

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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

#2
+94105
+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
#1
+4664
+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
+94105
+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
#3
+4664
+5

0.o

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

MathsGod1  Apr 23, 2015
#4
+92669
+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
+4664
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