Mathematics

[observer]

---

Okay, put your thinking caps on.

What is the sum of: 1 + 1/2 + 1/4 + 1/8 + 1/16 +....all the way to infinity?

* show also the steps to arrive at the answer.

[dbalagosa]

Okay, put your thinking caps on.

What is the sum of: 1 + 1/2 + 1/4 + 1/8 + 1/16 +....all the way to infinity?

* show also the steps to arrive at the answer.

Summation na bro

If unta ako lang mapakita dire pero ang symbols dili ko kahibaw unsaon

Summation of 1/(2^n), n=0, limit=infinity

Proof:
n=0, 1/2^0 = 1
n=1, 1/2^1 = 1/2
n=2, 1/2^2 = 1/4
n=3, 1/2^3 = 1/8
.............

[kobmat]

Okay, put your thinking caps on.

What is the sum of: 1 + 1/2 + 1/4 + 1/8 + 1/16 +....all the way to infinity?

* show also the steps to arrive at the answer.

Just looking at the series, i can tell that it will approach 2 as n approaches infinity.. Not sure if my proof below is correct.

[observer]

^ answer and the solution is correct.

The key to the problem is recognizing that it's a geometric series. So, to sum series like...a^0 + a^1 + a^2 +...+a^n,

Let S be the sum of that series to the nth term:

S = a^0 + a^1 + a^2 +...+a^n

so if I multiply both sides by a...

a*S = a^1 + a^2 +...+a^n + a^(n+1)

...if we subtract S from a*S, the resulting equation would look like

a*S - S = -a^0 + a^(n+1)
a*S - S = a^(n+1) - 1
S (a - 1) = a^(n+1) - 1
S = ( a^(n+1) - 1 ) / (a - 1)

Now, going back to that series stated in the problem, we can see that the series involves the term 1/2 with progressively increasing exponent. So we can apply our formula for this same scenario:

S = ( (1/2)^(n+1) - 1 ) / ( (1/2) - 1 )

now n, in this case, is infinity. So 1/2 raised to the power infinity essentially gives you zero, since the numerator will always remain as 1 and the denominator runs to infinity.

so,

S = ( 0 - 1 ) / ( -1/2 )
S = -1 / ( -1/2 )

...negative sign cancels out. And to divide by a fraction, you multiply the numerator with the reciprocal of the denominator

S = 1 * 2

S = 2

[kobmat]

I had to google it and make sense of all of it since i need a solution to the answer i had in my head which is 2. I have to admit im not that familiar with this, i had to take a path that is easy for me to understand. Sorry about that.

[observer]

Anyway, I want to know if anyone of you knows how to prove this particular Ramanujan Sum:

1 + 2 + 3 + 4 + 5 +...all the way to infinity = -1/12

I couldn't begin to wrap my head around this, but they say this is true.

Srinivasa Ramanujan actually wrote to his British correspondent, another great mathematician named G. H. Hardy:

Dear Sir, I am very much gratified on perusing your letter of the 8th February 1913. I was expecting a reply from you similar to the one which a Mathematics Professor at London wrote asking me to study carefully Bromwich's Infinite Series and not fall into the pitfalls of divergent series. … I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter

I think the proof would be quite lengthy. If anyone can explain how this sum is -1/12, I think we'd all be wiser as a result...hehe

[YanZi]

The title of this subject matter is: "DIVIDING ANY NUMBER BY 5"
Question: 14 / 5 = ?
Step 1: Double the first number. So, 14 x 2 = 28.
Step 2: Put a decimal before the ones digit in your Step 1 answer. So, 2.8
Answer: 2.8

Now try this: 67 / 5 = ?

[YanZi]

The title of this subject matter is: "MULTIPLY ANY NUMBER BY 9"
Question: 26 X 9 = ?
Step 1: Multiply the first number by 10. So, 26 x 10 = 260.
Step 2: Subtract the original number from the answer in step 1. So, 260 - 26 = 234
Answer: 234

Simple pero cool... Now try this: 38 X 9 = ?

[YanZi]

The title of this subject matter is: "MULTIPLY ANY NUMBER BY 99"
Question: 26 X 99 = ?
Step 1: Multiply the first number by 100. So, 26 x 100 = 2600.
Step 2: Subtract the original number from the answer in step 1. So, 2600 - 26 = 2574
Answer: 2574

Gets mo? Now try this: 49 X 99 = ?

Pwede rasad ni multiply any number by 999... Himo-a lang 1000 ang multiplier sa step 1.

[zxxc]

Math baya akong favorite subject..

Alot of times nga nahitabo nga ako ra og ang akong teacher sa math ang nagkasinabot..

D nagud ko tawgon sa easy or starter problem adto najud permi sa pinakalast problem/pinakalisud akoi pasolvon..

Best side of being math freak, alot of chix will stick on you..