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:
x = 4
Step-by-step explanation:
To solve this equation, first you want to write the whole thing out.
32x - 1 = 243
Next you want to get the variable by itself, so you are going to use inverse operations. in the equation, it is 32x - 1, so you are going to add one to both sides, getting you this:
32x = 244
Now for the final step you are going to get x alone, so you are going to use inverse operations once more and divide 32 on both sides getting you your answer.
x = 4
Now if you want to check your work simply plug in x, and if it is equal, you got the correct answer!
I hope this helped and good luck with your math!
I'm really sorry if I'm wrong though, even though I already finished this unit a while ago I struggled on this one even though it is so easy compared to the equations I have now.
Answer:
A. 6c = t
Step-by-step explanation:
- 6 c- chairs for each table.
- for example
- 3 table, so 6 chairs for each table 3 * 6 = 18.
2. 18 chairs for 3 tables.
Answer:
the maximum hours that they can rent it for is 8
Step-by-step explanation:
36 + 8.8t < 106.4
8.8t < 70.4
t < 8
Answer:
∠X in the pre-image will be equal to ∠L in the main image
Step-by-step explanation:
△LMN is the result of a reflection of △XYZ which means △LMN is the mirror image △XYZ
hence, the left of △XYZ will be equivalent to the right of △LMN and the right of △XYZ will be equivalent to the left of △LMN
Hence, ∠X in the pre-image will be equal to ∠L in the main image
