- #1
gat0man
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Homework Statement
This is not so much an entire problem I need help with but just a part.
It is a power series where after you do the ratio test, you end up with |4x^(2)| < 1, so |x^(2)| < 1/4.
Since the radius of convergence is |x-a| < R, I end up with -1/4 < x^(2) < 1/4, but because you cannot take the square root of a negative number, I get 0 <= x < 1/2
So how would I describe the Radius of Convergence in this case? Thanks in advance.
Homework Equations
|x-a| < R (but in this case after the ratio test you end up with 4x^(2) < 1)
The Attempt at a Solution
See what I wrote in AEDIT: You can delete this post, I was just spacing on some primary algebra :(
|x^2| < 1/4 -----> |x| < 1/2, -1/2 < x < 1/2 so radius of convergence is 1/2
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