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3 years ago

Determine if the following series converges or diverges. If it converges determine its sum.∞∑n=0 (−1)n

Mathematics

1 answer:

Tasya [4]3 years ago

3 0

Answer: The given series neither converges nor diverges.

Step-by-step explanation: We are given to determine whether the following series converges or diverges :

$S=\sum_{n=0}^{\infty}(-1)^n.$

If the series converges, we are to find its sum.

The given series can be written as :

$1,~-1,~1,~-1,~1,~1,~~.~~.~~.$

We note that the given series is a geometric one with first term 1 and common ratio given by

$r=\dfrac{-1}{1}=\dfrac{1}{-1}=~~.~~.~~.~~=-1.$

We know that a geometric series with common ratio r converges if |r| <1 and diverges if |r| > 1.

Since |r| = 1 for the given series, so the series will neither converge nor diverge.

Thus, the given series neither converges nor diverges.

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(05.04 MC) An image of a rectangular pyramid is shown below: A right rectangular pyramid is shown. Part A: A cross section of th

sleet_krkn [62]

Answer:

Part a) Rectangle

Part b) Triangle

Step-by-step explanation:

Part A) A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section?

we know that

When a geometric plane slices any right pyramid so that the cut is parallel to the plane of the base, the cross section will have the same shape (but not the same size) as the base, So, in the case of a right rectangular pyramid, the cross section is a rectangle

Part b) If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section?

we know that

Cross sections perpendicular to the base and through the vertex will be triangles

5 0

3 years ago

Help SHOW WORK PLEASE

stiv31 [10]

Answer:

1 ft./yr.

Step-by-step explanation:

When the question asks for rate of growth in a linear equation, we are going to look for slope. Slope formula is (y2-y1)/(x2-x1). We are given the points (2,5) and (5,8).

Now we can plug them into our formula:

(5-8)/(2-5)

-3/-3

Therefore, our rate of growth, or slope, is 1.

6 0

3 years ago

Solve the equation. Round to the nearest hundredth. Show work.

Burka [1]

Answer:

$x=-0.75$

Step-by-step explanation:

The given equation is

$4^{-5x-7}=6^{2x-1}$

We take logarithm of both sides to base 10.

$\log(4^{-5x-7})=\log(6^{2x-1})$

$(-5x-7)\log(4)=(2x-1)\log(6)$

We expand the brackets to get;

$-5x\log(4)-7\log(4)=2x\log(6)-\log(6)$

Group similar terms;

$-7\log(4)+\log(6)=2x\log(6)+5x\log(4)$

$-7\log(4)+\log(6)=(2\log(6)+5\log(4))x$

$\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x$

$x=-0.752478$

To the nearest hundredth.

$x=-0.75$

3 0

3 years ago

Rackham Graduate School has 8,000 students (5,000 PhD students and 3,000 masters stu- dents). The Rackham Student Government Exe

Free_Kalibri [48]

Answer:

a) 8,000!/(8000 - 4)! ways

b) 15,000,000 + 7998!/(7998 - 2)! ways

c) 5,000 + 7,999!/(7,999- 3)! ways

d) 3,000 + 7,999!/(7,999- 3)! ways

Step-by-step explanation:

The number of students at Rackham Graduate School = 8,000 students

The number of PhD students = 5,000

The number of masters students = 3,000

The number of student members of the Rackham Student Government Executive Board = 4 students

a) The number of ways there are to choose the Exec Board from all Rackham students = The number of ways to choose 4 students from 8,000 = 8,000!/(8000 - 4)!

b) The number of ways of having one Master student in the board = 3,000 ways

The number of ways of having one PhD student in the board after selecting a masters student = 5,000 ways

The number of ways of selecting the remaining 2 members =

7998!/(7998 - 2)!

The total number of ways of selecting at least one masters and one PhD in the board is therefore equal to 5,000 × 3,000 + 7998!/(7998 - 2)! ways

c) The number of ways of choosing the VP position as PhD = 5,000 ways

The number of ways of choosing the other three members = 7,999!/(8000 - 3)!

Therefore, the total number of ways = 5,000 + 7,999!/(7,999- 3)! ways

d) The number of ways of choosing a masters student as the VP position = 3,000 ways

The number of ways of choosing the other three members = 7,999!/(8000 - 3)!

Therefore, the total number of ways = 3,000 + 7,999!/(7,999- 3)! ways

8 0

3 years ago

Write the equation of the line containing points (5, 9) and (2, -9).

attashe74 [19]

Answer:

y=6x-21

Step-by-step explanation:

4 0

3 years ago