Question

Consider the infinite geometric series below. a. Write the first 4 terms of the series b. Does the series diverge or converge? c. If the series has a sum, find the sum. ∑ [infinity] n=2 (− 2) n−1

Answer 1

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 ±∞