3 3 votes The radius of convergence of the power series$$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$$ is: _____________ Calculus gate1993 calculus convergence normal out-of-gatecse-syllabus fill-in-the-blanks + – Kathleen 2.7k views answer comment Share Follow Print See all 12 Comments 12 12 Comments reply Show 9 previous comments ankitgupta.1729 commented Jul 21, 2019 reply Follow flag 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?? please check it : https://en.wikipedia.org/wiki/Radius_of_convergence#Theoretical_radius and u initialized m=0, but it can be m=1 too. right?? yes. 0 0 replyShare Satbir commented Jul 21, 2019 reply Follow flag its part of numerical methods which is no more in GATE CS syllabus. 0 0 replyShare srestha commented Jul 21, 2019 reply Follow flag @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. 0 0 replyShare Please log in or register to add a comment.
0 0 votes see the solution: syndie.byford answered Feb 4 syndie.byford comment Share Follow 0 reply Please log in or register to add a comment.
