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Sums of odd numbers (Zeta)


cindy 2005

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I already posted this one but in a wrong place - introduction section.

 

Here are the series formulas:

1 − 1╱3^25 + 1╱5^25 − 1╱7^25 + 1╱9^25 − + . . . = (3102906832711417381π^25)╱832751748218666596308929 7408000

 

1 − 1╱3^41 + 1╱5^41 − 1╱7^41 + 1╱9^41 − + . . . = (594046028724599200715086271256233100000π^41)╱1435 37334593793942723252075071256800000000000000000000 000000

 

If you cannot read, please see the attached file (OddNums.jpg) . Are the series formulas correct in math? (The last 5 zeros in the second series can be taken off but ...)

Thanks,

 

Cindy

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I already posted this one but in a wrong place - introduction section.

 

Here are the series formulas:

1 ? 1?3^25 + 1?5^25 ? 1?7^25 + 1?9^25 ? + . . . = (3102906832711417381?^25)?832751748218666596308929 7408000

 

1 ? 1?3^41 + 1?5^41 ? 1?7^41 + 1?9^41 ? + . . . = (594046028724599200715086271256233100000?^41)?1435 37334593793942723252075071256800000000000000000000 000000

 

If you cannot read, please see the attached file (OddNums.jpg) . Are the series formulas correct in math? (The last 5 zeros in the second series can be taken off but ...)

Thanks,

 

Cindy

 

I do know the series sum

 

sum (1/k^2) ~= (pi)^2 / 6 <= with a constant factor (from calculus I learnerd this)

 

So you are saying this came from the Zeta function ? Get Bo in to answer this... I am

curious. ;)

 

Maddog

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I already posted this one but in a wrong place - introduction section.

 

Here are the series formulas:

1 − 1╱3^25 + 1╱5^25 − 1╱7^25 + 1╱9^25 − + . . . = (3102906832711417381π^25)╱832751748218666596308929 7408000

 

1 − 1╱3^41 + 1╱5^41 − 1╱7^41 + 1╱9^41 − + . . . = (594046028724599200715086271256233100000π^41)╱1435 37334593793942723252075071256800000000000000000000 000000

 

If you cannot read, please see the attached file (OddNums.jpg) . Are the series formulas correct in math? (The last 5 zeros in the second series can be taken off but ...)

Thanks,

 

Cindy

 

If your question is "Are the series formulas correct in math? " only then answer is YES. Pls dont ask me to prove this ;)

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I do know the series sum

 

sum (1/k^2) ~= (pi)^2 / 6 <= with a constant factor (from calculus I learnerd this)

 

So you are saying this came from the Zeta function ? Get Bo in to answer this... I am

curious. ;)

 

Maddog

 

Thanks for your comments and thanks to others, too. The two series that I posted this web site are the ones I found by using Calculus technique. Currently, all zeta numbers are found except for odd numbers, for example, zeta(3), zeta(5)... It has been proved that the odd zeta numbers are irrational. If you take a look carefully on the series that I posted here, you see the + sign and -sign in each term that shows differences from zeta definition. If you cannot read it from text plain, you can download the jpg file in the attached of this web page.

 

I posted my results here in order for computer guys verify the results if they have a chance.

 

Thanks,

 

Cindy

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