Question

a. Write the first four terms of the series.

b. Does the series diverge or converge?

c. If the series has a sum, find the sum. Show your work.

Answer 1

Step-by-step explanation:

a. The first four terms are:

-4 (⅓)¹⁻¹ = -4

-4 (⅓)²⁻¹ = -4/3

-4 (⅓)³⁻¹ = -4/9

-4 (⅓)⁴⁻¹ = -4/27

b. This is a geometric series.  Since the absolute value of the common ratio is less than 1 (|⅓| < 1), the series converges.

c. The series converges to the sum of:

S = a₁ / (1 − r)

S = -4 / (1 − ⅓)

S = -6