What is the value of x? enter your answer in the box.
2 answers:
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I'm guessing the series is supposed to be
By the ratio test, the series converges if the following limit is less than 1.
The first
terms in the numerator's denominator cancel with the denominator's denominator:
also cancels out and the remaining factor of 
can be pulled out of the limit (as it doesn't depend on ).
which means the series converges everywhere (independently of
), and so the radius of convergence is infinite.
By the ratio test, the series converges if the following limit is less than 1.
The first
which means the series converges everywhere (independently of
If you're just integrating a vector-valued function, you just integrate each component:
The first integral is trivial since .
The second can be done by substituting :
The third can be found by integrating by parts: