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Hi.

I saw that there were a pair of threads that discussed these series but since it was far away from my knowledge I decided to start my own.

I have just been introduced to these series and found out that the series on the form of:

a_0 + a_1*x + a_2*x^2 + a_3*x^3 + ....

Where

a_0 = 1

a_1 = 0

a_2 = 1

a_3 = 0

a_4 = 1

...

Can be descirbed with the equation (1-x^2)^-1 as long as -1 ≤ x ≤ 1, i.e. it is convergence.

But I also read that even though the answers where x is either smallar than -1 or bigger than 1 seems like nonsens, this isnt the case. For example when x = 2 the author writes

Now in which way can -1/3 make any meaning when the series clearly goes to infinity?

I saw that there were a pair of threads that discussed these series but since it was far away from my knowledge I decided to start my own.

I have just been introduced to these series and found out that the series on the form of:

a_0 + a_1*x + a_2*x^2 + a_3*x^3 + ....

Where

a_0 = 1

a_1 = 0

a_2 = 1

a_3 = 0

a_4 = 1

...

Can be descirbed with the equation (1-x^2)^-1 as long as -1 ≤ x ≤ 1, i.e. it is convergence.

But I also read that even though the answers where x is either smallar than -1 or bigger than 1 seems like nonsens, this isnt the case. For example when x = 2 the author writes

That the equation,(1-x^2)^-1, gives.In fact, it is perfectly possible to give a mathematical sense to the answer -1/3

Now in which way can -1/3 make any meaning when the series clearly goes to infinity?

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