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The radius of convergence of the power series$$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$$ is:   _____________

But , it came in GATE . So, better to do. right??

I think syllabus of calculus was different that time. Please check some questions of 1993 below, It involved Fourier series, double integral etc.

With stirling formula it came 3. Then why radius of converge inverse the value??

and u initialized  m=0, but it can be m=1 too. right??

yes.

its part of numerical methods which is no more in GATE CS syllabus.

@ankitgupta.1729

@Satbir

Say, for an equation $a_{n}$, if the equation converges, then  $\lim_{n\rightarrow \infty}a_{n}=0.$ But here it comes $3,$ which means here function  diverges. So, to make it convergent, we inverses it.

right??

Please check some questions of 1993 below, It involved Fourier series, double integral etc.

limit, convergence-divergence, double integral is in syllabus. These thing are not out of syllabus. But fourier series not in syllabus now.

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