Question

What is the sum of the series sum from n equals 1 to infinity of negative 7 times three eighths to the n power question mark

a. eight thirds
b. negative twenty-one
c. fifths twenty-one
d. fifths negative
e. twenty-one elevenths

Answer 1

The sum of the given series is -11.2.

Step-by-step explanation:

The series given is ∑n=1 to ∞ of -7(3/8)^n. We can express this series as a geometric series. A geometric series has the form ∑n=0 to ∞ ar^n, where a is the first term and r is the common ratio. In this case, a = -7 and r = 3/8. The sum of a geometric series is given by the formula S = a / (1 - r). Substituting the values, we get S = -7 / (1 - 3/8) = -7 / (5/8) = -7 * 8/5 = -56/5 = -11.2.