Question says: [itex]\sum(cos(n*pi)/5^n)[/itex] from 0 to infinity. Proved that it converges: ratio test goes to abs(cos(pi*(n+1))/5cos(pi*n)) with some basic algebra. As n goes to infinity, this approaches -1/5 (absolute value giving 1/5) since cos(pi*(n+1))/cos(pi*n) is always -1, excepting the asymptotes. Question wants to find sum. Wolfram claims sum is 5/6 and won't elaborate. How?