hi can I ask if this series right or wrong. I found it with my calculations thanks

Mohammad Hammad

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Jul 11, 2019
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38
I see
and yes the sign is ulternate for negative integers side.
my post here is about if we but minus integer in the positive side of the equation.
for example if you put x=-5 in this positive side equation
Screenshot_٢٠٢١_١٠١٣_٢٠٣٤٢٩.png

you will get the answer having ln(2) according to wolfram language !!
why is that happen I don't know .
 

Dr.Peterson

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Nov 12, 2017
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12,598
I see
and yes the sign is ulternate for negative integers side.
my post here is about if we but minus integer in the positive side of the equation.
for example if you put x=-5 in this positive side equation
View attachment 29254

you will get the answer having ln(2) according to wolfram language !!
why is that happen I don't know .
But that's not what you put into WA! This has x+1, ... in the denominators, not x-1, ... as you showed.

You may include a link to your WA results, rather than an image, which may help us interact better.
 

Mohammad Hammad

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Jul 11, 2019
Messages
38
this equation have 2 formulas.
one for the positive integers which have (+) always.
and one for the negative integers which have alternative signs.
 

Mohammad Hammad

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Jul 11, 2019
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if we take the positive side with the positive integers it will work and the same for the negative side.
I was trying to take the positive side for the negative integers such as (x=-5) but it gave me logarithm 2 always. !!
 

Mohammad Hammad

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Jul 11, 2019
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38
so you can write it ..
1/x=(1/x1)(0!+(1/x2)(1!+(1/x3)(2!+(1/x4)(3!+(1/x5)(4!+(1/x6)(5!+...∞

where
x1=x+1
x2=x+2
x3=x+3 ...and so on.
 
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