Answer:
Step-by-step explanation:
Given the geometrical series
∑ [infinity] n=2 (− 2) n−1
I think the correct series should be the sum from n = 2 to ∞ of (-2)^n-1
So,
∑(-2)^(n-1)...... From n = 2 to ∞
A. The first four terms
When n = 2
(-2)^(2-1) = (-2)^1 = -2
When n = 3
(-2)^(3-1) = (-2)^2 = 4
When n = 4
(-2)^(4-1) = (-2)^3 = -8
When n = 5
(-2)^(5-1) = (-2)^4 = 16
B. The series will diverge since the common ratio is not between 0 and 1
So, let use limit test
Lim as n →∞ (-2)^(n-1) = (-2)^∞ = ±∞
Since the limit is infinite, then the series diverges
C. Since her series diverges we can find the sum, the sum is infinite, so it will sum up to ±∞
