1 votes 1 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-gate-syllabus fill-in-the-blanks + – Kathleen asked Sep 13, 2014 • recategorized Apr 22, 2021 by Lakshman Bhaiya Kathleen 1.2k views answer comment Share Follow See all 12 Comments See all 12 12 Comments reply Sherrinford commented Jul 19, 2019 reply Follow Share can someone please answer this question 0 votes 0 votes Satbir commented Jul 19, 2019 reply Follow Share What is written below the cursor in the image ? 0 votes 0 votes Sherrinford commented Jul 19, 2019 reply Follow Share 'm!' is written 0 votes 0 votes ankitgupta.1729 commented Jul 19, 2019 reply Follow Share @Satbir,@Sherrinford, starting value of 'm' is not given in the question. 0 votes 0 votes Sherrinford commented Jul 19, 2019 reply Follow Share lets assume m starts from zero 0 votes 0 votes ankitgupta.1729 commented Jul 20, 2019 reply Follow Share then answer will be $1/3$.. check here :- https://math.stackexchange.com/questions/3298415/radius-of-convergence-for-a-power-series 0 votes 0 votes Sherrinford commented Jul 20, 2019 reply Follow Share Thank you for Answer, are these of questions in GATE 2020 syllabus? 0 votes 0 votes ankitgupta.1729 commented Jul 20, 2019 reply Follow Share Radius of Convergence topic comes under power series which is a part of calculus. Since, power series is not mentioned in the syllabus, So, I guess chances are very less that these type of questions will be asked in gate but for other exams like ISI, TIFR etc, chances are very high :P 1 votes 1 votes srestha commented Jul 21, 2019 reply Follow Share But , it came in GATE . So, better to do. right?? 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?? 0 votes 0 votes ankitgupta.1729 commented Jul 21, 2019 reply Follow Share 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 votes 0 votes Satbir commented Jul 21, 2019 reply Follow Share its part of numerical methods which is no more in GATE CS syllabus. 0 votes 0 votes srestha commented Jul 21, 2019 reply Follow Share @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 votes 0 votes Please log in or register to add a comment.