- #1

asif zaidi

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__Problem Statement:__Compute the Taylor Series for (1+x)^1/2 and find the radius of convergence

Problem Solution:Problem Solution:

The Taylor Series expansion I get is

T(x) = 1 + (0.5*x) - (0.25*x^2)/2 + (0.375*x^3)/3! - (0.9375*x^4)/4! +...-...

So to get radius of convergence I have to find a closed solution form of the above equation and I simply am not able to come up with anything. Any pointers on this will be appreciated.

But then I was looking at the equation and saw that at least I can represent the x and the factorial portions as Sum (from 0-inf) x^i/i! and not worry about the coefficient.

If I use ratio test on this closed form, I will get the interval of convergence to be -inf to +inf. Therefore radius of convergence is +inf

Am I correct - if not please advise

Thanks

Asif