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## #1 2008-05-03 02:50:55

tony123
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### sum

Last edited by tony123 (2008-05-03 02:52:52)

TheDude
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Wrap it in bacon

## #3 2011-04-12 13:21:01

gAr
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### Re: sum

Hi,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

## #4 2011-04-20 20:41:46

alexa.pete9
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### Re: sum

Caushy Root Law is applicable on this question. And it can also be solved by applying the limits on it. The answer of the Question is 3.

## #5 2011-04-20 20:46:59

gAr
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### Re: sum

Can you show us how?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

## #6 2011-04-20 21:46:14

bobbym

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### Re: sum

Hi all;

I do not think there is much to show. You only have to sum the first 2 to see the sum is greater than 3.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #7 2011-05-12 05:21:03

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### Re: sum

Hi all;

I do not think there is much to show. You only have to sum the first 2 to see the  >> sum is greater than 3. <<

The above amendment comes right out of the first two consecutive terms, as well as
it shows 3 followed by an excess positive number.

This exemplifies the highlighted comment in the quote box.

Last edited by reconsideryouranswer (2011-05-12 05:45:19)

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## #8 2011-05-12 06:41:12

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### Re: sum

Break up the original sum into the sum of these separate parts:

sum (1 to oo) [(n^2)/(2^n)]:

Let S = 1/2 + 4/4 + 9/8 + 16/16 + ...

Then (1/2)S = 1/4 + 4/8 + 9/16  + ...

S - (1/2)S = 1/2 + 3/4 + 5/8 + 7/16 + ...

(1/2)S = 1/2 + 3/4  + 5/8 + 7/16 + ...

(1/4)S = 1/4 + 3/8 + 5/16 + 7/32 + ...

(1/2)S - (1/4)S = 1/2 + 2/4 + 2/8 + 2/16 + ...

(1/4)S = 1/2 + 2(1/4 + 1/8 + 1/16 + 1/32 + ...)

(1/4)S = 1/2 + 2(1/2)

(1/4)S = 1/2 + 2/2

(1/4)S = 3/2

4(1/4)S = 4(3/2)

S = 6

---------------------------------------------------------

sum (1 to oo) [(2n)/(2^n)]:

= 2[sum (1 to oo) (n)/(2^n)]:

= 2[1/2 + 2/4 + 3/8 + 4/16 + ...] **

Let S = 1/2 + 2/4 + 3/8 + 4/16 + ...

(1/2)S = 1/4 + 2/8 + 3/16 + ...

S - (1/2)S = 1/2 + 1/4 + 1/8 + 1/16 + ...

(1/2)S = 1

2(1/2)S = 2(1)

S = 2

Then ** = 2[2]

= 4

---------------------------------------------------------

sum (1 to oo) [3/(2^n)]:

= 3[sum (1 to oo) 1/(2^n)]

= 3[1/2 + 1/4 + 1/8 + ...]

= 3[1]

= 3

--------------------------------------------------------

Then the sum equals

6 + 4 + 3 =

13

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