Infinite tangent series - Oxford Mathematics Admissions Test 2020

[@RajSandhu-gm8iz]

Your logic and reasoning was spot on. It is 1 solution. I got it wrong, said it was 2 solutions, I forgot |r| has to be

[@mathoutloud]

It would be easy to forget to reject one of the roots. But as a good rule of thumb, once you identify the infinite geometric series you should also have a flag pop up in your head about the domain where it is convergent. Will help to avoid needless mistakes. Trust me, I’m an expert in those!

[@dan-florinchereches4892]

Lol I don't think you are alone

[@RajSandhu-gm8iz]

@@mathoutloud Noted!!

[@dan-florinchereches4892]

I see this infinite series being x+x^2+x^3+...=1/(1-x) when |x| 1 and tan(x)=(by condition) 1/tan(x) +1/tan^2(x)+...=1/(1-tanx) => tan(x)-tan^2(x)=1 or tan^2(x)-tan(x)+1=0 Tan(x)=(1+-sqrt(5))/2 we reject tan(x)=(1-sqrt(5))/2 because it is not smaller than -1 so we are left with one choice