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 <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
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: The answer is F.
Step-by-step explanation:
1.) The first equation represents how the spiral notebook has 30 more pages than the the memo book, and how subtracting the memo book's pages would result with 30.
2.) The second equation represents how the total number of pages in 3 spiral notebooks plus 5 memo books would result in 810 total pages.
Answer:
A square field has a perimeter if 3.6km what is the length of one side in metres
Step-by-step explanation:
A square field has a perimeter if 3.6km what is the length of one side in metres
Answer:
80
Step-by-step explanation:
Angle VSU = 100. Angles TSU is a linear pair with angle VSU so adding them together equals 180. 180-100=80.
A confidence interval tells us how many percents we are confident about the range of a parameter. In this problem, <span>a 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). That means we're 95% confident that the Americans spend from 1.38 hours to 1.92 hours per day on average relaxing or pursuing activities they enjoy. In other words, 95% of the samples of the same size would have a mean number of hours relaxing or pursuing activities they enjoy between 1.38 to 1.92.</span>
