Question

cotg ($\pi/3+ \pi/6+ \pi /12...)$ ) e uma p.g

Answer 1

Olá Wenne 

cotg(π/3 + π/6 + π/12 + ...)

u1 = π/3
u2 = π/6

q = u2/u1 = (π/6)/(π/3) = 1/2

soma infinita
Si = u1/(1 - q)
Si = (π/3)/(1 - 1/2) = 2π/3

cotg(π/3 + π/6 + π/12 + ...) = cotg(2π/3) = -√3/3