Consider the infinite geometric series below. a. Write the first 4 terms of the series b. Does the series diverge or converge? c. If the series has a sum, find the sum. ∑ [infinity] n=2 (− 2) n−1
Answers
Answer:
Step-by-step explanation:
Given the geometrical series
∑ [infinity] n=2 (− 2) n−1
I think the correct series should be the sum from n = 2 to ∞ of (-2)^n-1
So,
∑(-2)^(n-1)...... From n = 2 to ∞
A. The first four terms
When n = 2
(-2)^(2-1) = (-2)^1 = -2
When n = 3
(-2)^(3-1) = (-2)^2 = 4
When n = 4
(-2)^(4-1) = (-2)^3 = -8
When n = 5
(-2)^(5-1) = (-2)^4 = 16
B. The series will diverge since the common ratio is not between 0 and 1
So, let use limit test
Lim as n →∞ (-2)^(n-1) = (-2)^∞ = ±∞
Since the limit is infinite, then the series diverges
C. Since her series diverges we can find the sum, the sum is infinite, so it will sum up to ±∞
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2x + y ≤ 8
2x - 5y < 20
Answers
Answer: answer below.
Step-by-step explanation:
To solve this system of linear inequalities, we can use a graphical method or algebraic method.
Let's start with the algebraic method.
First, let's rearrange the inequalities to solve for one variable in terms of the other.
From the first inequality, we have:
x ≤ 10 - 2y
From the second inequality, we have:
y ≤ 8 - 2x
From the third inequality, we have:
x ≤ (20 + 5y)/2
Now, let's plot the graphs of these inequalities on a coordinate plane.
Graphing the first inequality, x ≤ 10 - 2y, we start by drawing the line x = 10 - 2y. Since it is a "less than or equal to" inequality, we will draw a solid line.
Graphing the second inequality, y ≤ 8 - 2x, we start by drawing the line y = 8 - 2x. Again, since it is a "less than or equal to" inequality, we will draw a solid line.
Graphing the third inequality, x ≤ (20 + 5y)/2, we start by drawing the line x = (20 + 5y)/2. This time, since it is a "less than" inequality, we will draw a dashed line.
Now, we shade the region that satisfies all three inequalities. This region is the intersection of the shaded regions of the individual inequalities.
Finally, we can determine the solution by looking at the shaded region on the graph. The solution is the set of all points that lie within or on the boundary of the shaded region.
Alternatively, we can also solve the system of inequalities algebraically by finding the points where the lines intersect. We can then check if these points satisfy all three inequalities.
20(−1.5r+0.75)
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(B) the population after time
(C) the rate of increase
(D) the time
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Answer:
It's D.
Step-by-step explanation:
D. The t s the time where t = 0 corresponds to the initial population.
Answers
=
= 490.87
Area of Oven tray= 60cm x 50cm
= 3000
: . # tin that can hold on bake tray= 3000
Thus making it logically 6.....
3.24 m
32.4 m
3,240 m
3,240 m
Answers
: . 324 cm to m =
thus A
Answers
Answer:
The length of segment of OL is 22.4 cm
Option 3 is correct
Step-by-step explanation:
In ΔMNL, NM||PO
If two sides are parallel then their corresponding sides are in ratio.
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in same ratio.
Therefore,
OL = x+4
OL = 18.4 + 4 = 22.4 cm
Hence, The length of segment of OL is 22.4 cm
X+4 8
----- = ---- Now cross multiply to get 5x+20=112. 112-20= 92, and
14 5 92/5= 18.4. Your answer is A, 18.4 cm.
Hope this helps! :)