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:
v = 6
Step-by-step explanation:
Solve for v:
-8 (8 v + 1) - 2 = -394
-8 (8 v + 1) = -64 v - 8:
-64 v - 8 - 2 = -394
Grouping like terms, -64 v - 8 - 2 = -64 v + (-8 - 2):
-64 v + (-8 - 2) = -394
-8 - 2 = -10:
-10 - 64 v = -394
Add 10 to both sides:
(10 - 10) - 64 v = 10 - 394
10 - 10 = 0:
-64 v = 10 - 394
10 - 394 = -384:
-64 v = -384
Divide both sides of -64 v = -384 by -64:
(-64 v)/(-64) = (-384)/(-64)
(-64)/(-64) = 1:
v = (-384)/(-64)
The gcd of -384 and -64 is -64, so (-384)/(-64) = (-64×6)/(-64×1) = (-64)/(-64)×6 = 6:
Answer: v = 6
<span>The price usually goes up. If lots of people want something, you have to pay more to get it.</span>
I got 41.4 lbs if you round to the nearest tenths
Answer:
Cost =$3
Amount = 8 gallons and 17 gallons
Step-by-step explanation:
Given
24 + 51
Required
Simplify to show the cost and amount of gas bought by each individual
24 + 51
[Factorize]
3(8 + 17)
The above can't be factored any further.
Since the cost of gas for both individuals is the same, we can conclude the following.
Cost = $3
This is so because it applies to both numbers in brackets
Amount of Gas = 8 gallons and 17 gallons respectively by both individuals
