Find the sum of the infinite series
(tanx)^2-(tanx)^4+(tanx)^6+...+(see attached)
whenever the series converges

Question

anonymous · Answer

attachment

anonymous · Answer

I thought it was -(cosx)^2 but got the wrong answer

anonymous · Answer

Nah looks good http://www.wolframalpha.com/input/?i=sum+from+n%3D0+to+infinity+of+%28-1%29%5E%28n%2B1%29+%28tanx%29%5E%282n%29

anonymous · Answer

Yeah wolfram says it but it's not the answer that my online worksheet is looking for, I was looking for something perhaps it got wrong or misinterpreted

anonymous · Answer

Ah. Sum is done from n=0 which gives a 1 term in the series that shouldn't be there. The first term is tan^2(x)

anonymous · Answer

So that means it we got an answer to which -1 was added. So if we account for that and add a 1. We get 1-cos^2(x) = sin^2(x)

anonymous · Answer

wow I can't believe that I didn't catch that, thank you so much

anonymous · Answer

No problem. It caught me too :p