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I'm trying to find the radius of convergence for

$(x-2)^n/(2x+1)

I did the ratio test and ended up with:

absolute value[(x-2)/(2x+1)]<1
How would I solve for the inequality at this point?

1 answer

If |(x-2)/(2x+1)| < 1 then
(x-2)^2 < (2x+1)^2
x^2 - 4x + 4 < 4x^2 + 4x + 1
3x^2 + 8x - 3 > 0
x < -3 or x > 1/3

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