Answer:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
To answer this question, we let x be the the consulting fee of Iris. With this representation, the value for the hourly rate is equal to 11x. The equation that would allow us to relate the consulting services fee, hourly fee and total value given that she worked for 7 hours would then be equal to,
x + (7)(11x) = 470
Simplifying the left-hand side of the equation,
78x = 470
Dividing the equation by 78 will give us an answer of 6.
Hence,
<em> x = $6 (Consulting services fee)</em>
<em> 11x = 11($6) = $66 (hourly rate)</em>
120+10+5=135
I don't know if all you're supposed to do is add or not... so i may be wrong....
