Answer: Sum is 1.5
Explanation:
This is a Geometric series, with common ratio : r = -1/3
The formula for the nth term is: a(sub n) = a(sub 0) * r^n, a(sub 0) is the first term
Here: a(sub n) = 2 * (-1/3)^n
Because |r| < 1, we can use the sum formula
S = a(sub 0) * (r^(n+1) - 1)/(r - 1)
n gets really big, so r^(n+1) = 0
S = a(sub 0) * (-1)/ (r - 1)
S = 2 * (-1) / ( -1/3 - 1)
S = 2 / (4/3) = 2*3/4 = 3/2
Infinite sum is 3/2 = 1.5
From MysticAlanCheng