What is the series X + 1(1/x + 1/x^2 + 1/x^3 ...)?

[David George]

I have no math training beyond high school 45 years ago, and I don’t remember much of it. However I am doing a project, and I find the series below is quite valuable. But I do not know what it is or what it is called. It is like this:

X + 1 (1/x + 1/x^2 + 1/x^3 . . . ).

It comes ever closer to a value which is very significant in what I am doing. I wonder if someone can tell me what this is called, and what it can be used for.

 

[rock.freak667]

Well what is in the brackets is a geometric progrssion

 

[Avodyne]

Yes, the part in parentheses is a geometric series that can be summed (provided the absolute value of x is bigger than 1):

1/x + 1/x^2 + 1/x^3 + ... = 1/(x-1)

 

[David George]

Thank you!

 

[rock.freak667]

Yes, the part in parentheses is a geometric series that can be summed (provided the absolute value of x is bigger than 1):

1/x + 1/x^2 + 1/x^3 + ... = 1/(x-1)

For that sum to converge,

|1/x|<1