Limiting Sum Question!! (1 Viewer)

[Newbit]

Hey Guys, I'm having some trouble solving this question.
For the Geometric Series r= -tan^2(Theta)
For what values of theta in the interval -Pi/2 < Theta < Pi/2 does the limiting sum of the series exist?

 

[Carrotsticks]

A limiting sum exists if -1 < R < 1.

-1 < - tan^2 (x) < 1

But - tan^2 (x) < 1 for all real x, so the inequality is essentially:

-1 < - tan^2 (x) <= 0

Or to re-write it:

0 <= tan^2 (x) < 1

-1 < tan(x) < 1

- pi/4 < tan(x) < pi/4.