Formula for finding the radius of convergence of a power series

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[teddonaville]

wow you are pretty good at math, well done!

[gurkiratsinghtha]

Please make a video on the hardest putnam exam problems involving convergence tests and calculus.

[mathsandsciencechannel]

Great video.. I solved something similar and it's fun

[Θρησκόληπτος]

Help!!! I have this problem: Given a random ellipse and a fixed point P on it. Draw two perpendicular chords PA and PB of the ellipse. Then, no matter which chords you draw, AB will always pass through a certain point. (A.k.a. all possible ABs concur).
I know exactly what to do (e.g Pick the ellipse centered at zero for calculation purposes WLOG, find the general equation of AB which is not hard (perpendicular lines have slopes m1*m2=-1), which finally depends on one parameter m and prove that the system of 3 of them always has a solution (which reduces to a 3*3 determinant being equal to 0). The problem is that calculations are so, SO filthy that I am losing concentracion because I need (eg fraction bars longer than the width of a page). I even tried another way of choosing P(0, 0) and the PA, PB as the axes but the ellipse then becomes general and there is no better hope. Does the Professor really expect us to do extreme algebra in a Geometry class? I mean spending a whole afternoon distributing term by term and not even reducing anything? Try it out for yourselves. Is there an other placement that eases the problem? Polar coordinates (Although we haven't covered them yet)? What else can I do?

[bartomiejpotaman]

4:05 you can’t draw such conclusion. Counter ex: x<5 and x<7 it clearly doesn’t imply 5=7.