Calculus

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please help me...for the power series summation of n^4x^n/2(n-1)factorial....find the radius
i am guessing the radius is either x or x/2 but i am still not sure..CAN someone help me plz?

PLZ HELP ME...i don't know where to start

Take the ratio of two succesive terms and take the limit n --> infinity. For finite x the limit is zero, which means that the radius of convergence is infinity. In general, the radius of convergence is that value for x you have to substitute in the above limit to make it equal to 1. In this case the limit is zero for all x.

so the radius would be x right?

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