All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
Multiply both sides by r :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Answer:
Option A- 1.8x – 10 = –4; x = 1.8 x minus 10 equals negative 4; x equals StartFraction 10 Over 2 EndFraction.
Answer:
1,800 parts per hour
Step-by-step explanation:
330 parts = 11 min
330/11=30
30 parts = 1 min
60 min = 1 hour
30x60min=1,800
1,800 parts per hour
Answer:
$2268
Step-by-step explanation:
Luna's total mortgage payments for the year would be
... (monthly payment)×(number of months in a year)
... = $2100×12 = $25,200
Of that, 9% went to interest, so the interest amount is ...
... $25,200×9% = $2268
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<em>About percentages</em>
Your calculator may do percentages directly. If not, it can be helpful to realize that the percent symbol (%) means the same thing as /100 (divided by 100). So, 9% = 9/100 = 0.09
