Question

What is the sum of this infinite geometric series? Use the formula (s_n = raca_11-r) where (a_1) is the first term and (r) is the common ratio. The series is given by (sum_k=0^infty -20 left(0.75

ight)ᵏ)?

Answer 1

The sum of the infinite geometric series Σk=0∞ -20(0.75)k is -80, found by using the infinite geometric series sum formula with a first term of -20 and a common ratio of 0.75.

Step-by-step explanation:

The sum of the infinite geometric series Σk=0∞ -20(0.75)k can be found using the formula for the sum of an infinite geometric series: sn = a1 / (1 - r), where a1 is the first term and r is the common ratio. In this series, a1 = -20 and r = 0.75. Since |r| < 1, the series converges, and we can use the formula to find the sum. Substituting the values, we get s = -20/(1 - 0.75). Therefore, s = -20/0.25, which simplifies to s = -80.