Asked by alejandro
Determine the sum of the following geometric series. Round your answers to 4 decimals if necessary.
a) 50 over sigma k=1 8(.5)^k-2
a) 50 over sigma k=1 8(.5)^k-2
Answers
Answered by
Steve
I assume you mean
50
∑ 8(.5<sup>k-2</sup>)
k=1
In that case S<sub>50</sub> = a(1-r)^50/(1-r)
r = .5
a = 8(1/2^-1) = 16
S<sub>50</sub> = 16(.5^50)/.5 = 2^4 * 2^-50 * 2^1 = 2^-45 or 1/2^45
50
∑ 8(.5<sup>k-2</sup>)
k=1
In that case S<sub>50</sub> = a(1-r)^50/(1-r)
r = .5
a = 8(1/2^-1) = 16
S<sub>50</sub> = 16(.5^50)/.5 = 2^4 * 2^-50 * 2^1 = 2^-45 or 1/2^45
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