The sequence diverges because the value of the absolute common ratio r is greater than the 1.
<h3>What is convergent of a series?</h3>
A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We have series:
9, 27, 81, 243....
The above series is a geometric progression with common ratio r is 3
r = 3
We know the formula for a geometric sequence:
A geometric series converges only if the absolute value of the common ratio:
r < 1 and
It diverges if the ratio ≥ 1
Here the value of r = 3 which is greater than the 1 so the sequence diverges.
Thus, the sequence diverges because the value of the absolute common ratio r is greater than the 1.
Learn more about the convergent of a series here:
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Answer:
A, B
Step-by-step explanation:
Volume: the measure of the amount of space that a substance (such as liquid, gas, or solid) occupies in an enclosed environment (such as a container).
y=8(x^2 + 4x + 4) +17 + -32
Simplify:
y = 8(x^2 + 4x + 4) + 15
Use distributive property:
y = 8x^2 + 32x +32 - 15
Simplify:
y = 8x^2 + 32x +17
Complete the square using form ax^2+bx+c:
a = 8, b = 32, c = 17
vertex form = a(x+d)^2+e
d = b/2a and e = c-b^2/4a
d = 32/2*8 = 32/16 = 2
e = 17 - 32^2/4*8 = 17-1024/32 = 17-32 = -15
Vertex form = y = 8(x+2)^2 + -15
Answer:
11/15
Step-by-step explanation:
There are 8 marbles total. If they are being selected from twice with one missing, we could add 8 and 8 - 1 together to get the denominator for the probability.
8 + (8 - 1) = 15
We have to assume the first marble taken was red, so we will have 6 plus 6 - 1 red marbles to choose from for our numerator.
6 + (6 - 1) = 11
The probability of consecutively selecting two red marbles is 11/15.
Answer:
Each shirt costs $ 10, while each short costs $ 15.
Step-by-step explanation:
Since two brothers went shopping at a back to school sale where all shirts and shorts are the same price, and the younger brother spent $ 175 on 7 new shirts and 7 pairs of shorts while the older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $ 165, to determine the price of each shorts and each shirt the following system of equations must be considered:
Shirt = X
Short = Y
7X + 7Y = 175
6X + 7Y = 165
7X - 6X + 7Y - 7Y = 175-165
X = 10
7x10 + 7Y = 175
70 + 7Y = 175
7Y = 175 - 70
Y = 105/7
Y = 15
Thus, each shirt costs $ 10, while each short costs $ 15.