The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.
<h3>Find the radius of convergence R and the interval of convergence:</h3>
Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
= β
- If β < 1, then the series converges
- If β > 1, then the series diverges
- If β = 1, then the series inconclusive
Here aₙ = (n²/n!) xⁿ⁺³ and aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴
Now limit is taken,
= 
= 
= 
= 
= 0 < 1
Since the limit is less than 1 the series is converging.
We get that,
interval of convergence = (-∞, ∞)
radius of convergence R = ∞
Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.
Learn more about power series here:
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X = greater than or equal to six
Because you divide the 6 from each side
6x > 36
-----------
6. 6
Which equals x = greater than or equal to six
It has to be greater than or equal to because it had the line under it which means equal to and has the open mouth of the comparison sign facing the left which is greater than. Combine them together
Recall that perimeter of a rectangle can be expressed by 2l + 2w = p, in which l is the length and w is the width.
If the perimeter of a rectangle is 24 inches, we can plug that into the equation and we get the following:
2l + 2w = 24
Now, using the other bit of info, that the length is twice the width, we can create a second equation:
l = 2w
Now, we can plug in l into our value for 2w in our original equation using substitution.
2l + l = 24
By combining like terms, we get this:
3l = 24
Now if we divide both sides by 3, we get that the length equals 8.
Now we can plug 8 into our original equation in place of l.
2(8) + 2w =24
16 + 2w = 24
Subtract 16 from both side:
2w=8
Divide both sides by 2:
w=4
Now we have both the length and the width! We also know that the values are correct because 8, the length, is two times 4, the width.
Now we need to multiply these together to get the area.
8 x 4 = 32
And there you have it! 32 square units is the area.
Total eaten pizza = 2/8 + 3/8 = 5/8
Left pizza = 1 - 5/8 = 3/8
In short, Your Answer would be 3/8
Hope this helps!
Answer:
1. D. ray PS
2. C. angle GFE
3. A. 30 deg
Step-by-step explanation:
1. To name a ray, use two points on the ray. The first point must be the endpoint. The second point can be any point on the ray.
ray PS and ray PT are both correct.
Choose D. ray PS
2. Two ways of naming an angle are: 1. Use just the vertex point. 2. Use three points: a point on one ray, the vertex, a point on the other ray in that order.
This angle can be named:
angle EFG
angle GFE
angle F
Choose C. angle GFE
3. Angles CBE and ABD are vertical angles. Vertical angles are congruent. They have the same measure. Since angle ABD measures 30 deg, then angle CBE also measures 30 deg.
Choose: A. 30 deg
