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:
(-3,-1)
Step-by-step explanation:
Answer:
22 m
Step-by-step explanation:
The computation of the how much far does the boat travel is as follows:
sin 43 degrees = 15 ÷ d
d = 15 ÷sin 43 degrees
= 15 ÷ 0.6820
= 21.99
= 22 m
Hence, the how much far does the boat travel is 22 m
We simply applied the above formula so that the correct value could come
The same is to be considered
Answer:
2.50000 or 2.5 or 2 1/2
Step-by-step explanation:
You have the number 250,000. you have to get the decimal between 1.00 and 10.00 to do this we are going to move the decimal over left one at a time.
25,000.0
2,500.00
250.000
25.0000 25 is really close but not between 1 and 10 so were going to move the decimal one more time
2.50000
2.50000 is between 1 and 10 so its the anwser we are looking for.
A1 = 0.91
a6 = -0.14
sum = (0.91+-0.14) /2
sum = 2.31
