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April 18, 2014

Homework Help: math

Posted by mathstudent on Tuesday, February 10, 2009 at 3:20pm.

I read from my textbook:

If S is the infinite series 1 + x + x^2 + x^3 + ...
Then Sx = x + x^2 + x^3 + x^4 + ... = S - 1
So, S = 1/(1-x)

I follow what that logic, but it still doesn't make sense.
The way I see it, if you plug any real number > 1 into x, S will be infinity which does not equal 1/(1-x) at all...

For example, if I plug the constant 10 in for x,
The infinite series "1 + x + x^2 + x^3 + ..." will be infinity
yet 1/(1-x) will equal -1/9.

Can someone explain this?

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