Answers
Answer:
The convergent series are;
[tex]\sum \limits _{n = 1}^\infty \left( \dfrac{1}{5} \right) ^n[/tex]
(And)
[tex]\sum \limits _{n = 1}^\infty \left( \dfrac{1}{10} \right) ^n[/tex]
Step-by-step explanation:
A series in mathematics is the sum of a sequence of numbers to infinity
A convergent series is a series that sums to a limit
From the given options, we have;
First option
[tex]\sum \limits _{n = 1}^\infty \dfrac{2\cdot n}{n + 1}[/tex]
As 'n' increases, 2·n becomes more larger than n + 1, and the series diverges
Second option
[tex]\sum \limits _{n = 1}^\infty \dfrac{n^2 - 1}{n - 2}[/tex]
As 'n' increases, n² - 1, becomes more larger than n - 2, and the series diverges
Third option
[tex]\sum \limits _{n = 1}^\infty \left( \dfrac{1}{5} \right) ^n[/tex]
As 'n' increases, [tex]\left( \dfrac{1}{5} \right) ^n[/tex], becomes more smaller and tend to '0', therefore, the series converges
Fourth option
[tex]\sum \limits _{n = 1}^\infty \left( \dfrac{1}{10} \right) ^n[/tex]
As 'n' increases, [tex]3 \times\left( \dfrac{1}{10} \right) ^n[/tex], becomes more smaller and tend to '0', therefore, the series converges
Fifth option
[tex]\sum \limits _{n = 1}^\infty \dfrac{1}{10} \cdot (3) ^n[/tex]
As 'n' increases, [tex]\dfrac{1}{10} \cdot (3) ^n[/tex], becomes more larger and tend to infinity, therefore, the series diverges.
Answer:
C and D
Step-by-step explanation:
Edge 2021
Related Questions
The top of a storage container is a hemisphere with a diameter of 28 feet. What is the volume of the storage container? Round your answer to the nearest tenth
Answers
Answer:
5749.3 cubic feet
Step-by-step explanation:
The volume of the storage container would be defined by the volume of the shape; a hemisphere
The volume V of a hemisphere is given as
V = 2/3 π r^3
where r is the radius of the hemisphere
Given that the diameter is 28 feet, the radius = 14 feet
hence the volume
= 2/3 * π * 14^3
= 5749.333333
To the nearest tenth
= 5749.3 cubic feet
Can someone help me do this like the equation?!.
Answers
Answer:
36$
Step-by-step explanation:
What is the circumference of the circle? d=44in
Answers
Answer:
138.23 in
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
138.16
Step-by-step explanation:
Diameter times pi gives you circumference. I used 3.14
What is -11 2/3x(-4 1/5)
Answers
Answer:
49x
Step-by-step explanation:
Answer:
-49x
Step-by-step explanation:
-11 2/3x (-4 1/5)
= -49x
Sydney buys a new car for $24,000 and finances the car for 5 years at 2.5% interest compounded yearly. She estimates that the value of the car will decrease by 16% each year. If Sydney is able to sell the car on the day of her last car payment for the value she estimated, how much money will she have spent over the 5 years?
Answers
Answer:17,117
Step-by-step explanation:
which set of anges can form a triangle
Answers
Answer:
I didn't understand this but I can give you this info
Sum of all angles in a triangle = 180°
Which of these are factors of 16?
In geometry
Answers
Answer:
in geometry to find the factors of 16 we have to find numbers that can divide and without a number remaining 1,2,4
x) sec’A + cosec?A
secA. cosecA
Answers
Answer:
(Sin A + Cos A)/Sin A. Cos A
Step-by-step explanation:
As we know
Sec A = 1/Cos A
and Cosec A = 1/Sin A
Given Equation
Sec A + Cosec A
Substituting the given values, we get -
1/cos A + 1/Sin A
(Sin A + Cos A)/Sin A. Cos A
I am in need for help please
Answers
Answer:
x = 12
Step-by-step explanation:
Exterior angles thm:
8x - 10 + 5x - 12 = 134
13x - 22 = 134
13x = 134 + 22
13x = 156
x = 12
CODES Use the following information to solve. A bank gives each new customer a 4-digit code number which allows the new customer to create
their own password. The code number is assigned randomly from the digits 1, 3, 5, and 7, and no digit is repeated.
• What is the probability that the code number will start with 371?
a 1/3
b 1/4
с 1/12
d 1/24
Answers
=============================================================
Explanation:
There are 4 digits to pick from and 4 slots to fill, so there are 4! = 4*3*2*1 = 24 different codes possible.
If we want the code to start with 371, then that must mean 5 is the only thing left for that fourth slot. In short, there's only one code that starts with 371 and that code is 3715
We have one code we want (3715) out of 24 total, which is why the answer is 1/24 (choice D)
estimate a 15% tip for a 19.80 meal.
Answers
19.80 x 0.15 = 2.97
Answer:
$3.00
Step-by-step explanation:
The tip would equal to $2.97 so the answer is $3.00 that is your estimate
what is the answer to my problem
Answers
find the product.
enter your answer in simplest form.
6x2/3 = _=_
Answers
Step-by-step explanation:
6 • 2/3 =
12/3 =
4
Find the following trigonometric values,rounded to 4 decimal places: 1) tan45. 2)sin70. 3) cos30. 4) cos20
Answers
2) Sin70 = 0.9397
3) Cos30 = 0.8660
4) Cos20 = 0.9397
A secretary works a 35-hour week for which she is paid $262.50. If in a particular week she works 6 hours overtime on Saturdays which is paid for at time - and - a - half and 4 hours overtime on Sunday which is paid for a double time. calculate her gross wage for that week
no links please
Answers
Answer:
$390
Step-by-step explanation:
262.50/35 = 7.5 per hour during normal week
Saturdays 11.25 per hour
Sundays 15 per hour
6x11.25 = 67.5
4x15=60
262.50 +67.5 +60 = 390
Find the slope between:
(-3,5)
(1,-1)
Answers
Eddie needs to paint a fence which has 10,000 square feet of surface. One gallon of paint covers 600 square feet.
How many whole gallons of paint will he need?
Answers
Answer:
17
Step-by-step explanation:
10000/600=16.67
Find the missing number to make these fractions equal.
2/8 = ?/4
Answers
Answer:
?= 1
Step-by-step explanation:
Answer:
Step-by-step explanation:
let the missing number be x
2/8=x/4(do cross multiplication)
8*x=4*2
8x=8
x=8/8
x=1
please help with this one
Answers
Answer:
1st and 2nd to last
Step-by-step explanation:
Answer:
x< -3 is correct answer...........
a cylindrical tinfull of engine oil has a diameter of 12cmand the height of 14cm.the oil is poured into a rectangular tin 16cm long and 11cm wide,what is the depth of the oil in the tin?
Answers
Find the volume of the cylinder using the formula v = pixr^2 x height
V= 3.14 x 6^2 x 14 = 1,582.56 cubic cm
Area of of the rectangle = 16 x 11 = 176 square cm
The height will be the volume divided by the area
Height =1582.56/176 = 8.99 cm
The height is 8.99 cm ( round off as needed)
Blaine's take-home pay is $2,500 each month, and he has created a monthly budget to become more aware of where his money goes. His budget is shown below. Blaine finds that he can join a cheaper gym for $40/month, reduce his spending money to $200, and find a phone and internet package for $175. How much will these choices save him each month?
Answers
Answer:
Amount Blaine save = $250
Step-by-step explanation:
Total take home pay = $2,500
Original budget:
Rent + electricity bills = $990
Food/groceries = $525
Gas + insurance = $320
Spending money = $235
Cellphone + Internet = $250
Gym membership = $180
Total = $2,500
New budget:
Rent + electricity bills = $990
Food/groceries = $525
Gas + insurance = $320
Spending money = $200
Cellphone + Internet = $175
Gym membership = $40
Total = $2,250
How much will these choices save him each month?
Amount Blaine save = Total take home - new budget
= $2,500 - $2,250
= $250
Amount Blaine save = $250
The topic is about secant tangle anges
Answers
The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
Identify the slope of the line
y=-4- 1/6x
Answers
y=-1/6x-4
slope= -1/6
Plz help me with these 2 questions
Answers
9514 1404 393
Answer:
C = πd = 2πr
1. C = 18.84 m
2. C = 43.96 ft
Step-by-step explanation:
The formula to find the circumference is C = πd = 2πr.
__
1. C = 2π(3 m) = 6π m = 6(3.14) m = 18.84 m
__
2. C = πd = (3.14)(14 ft) = 43.96 ft
I need some help plz
Answers
Answer:
B : both containers are 50
Step-by-step explanation:
Since water in container 2 is in higher temp, it will transfer some of its heat to container 1 until both the containers reach same temperature. This is the concept of equilibrium that mother nature abides by.
The value of the square root of 25+144 is 13. True or false
Answers
Answer:
true i tested it out myself.
Step-by-step explanation:
hey! i’ll give brainliest please help
Answers
Answer:
It's the second one, two independent clauses connected by a conjunction
Based on the table,what is the volume,in litters,of sample 2?
Answers
0.65 / 0.5 = 5.2 / ?
1.3 = 5.2 / ?
? = 5.2 / 1.3
? = 4 Liters
What is the domain of the function
Answers
Answer:
third answer is correct
Step-by-step explanation:
Ryan has 10 quarters.
Kelly has exactly seven times as much money as Ryan.
They will combine their money to buy a game.
The game costs $27. How much more money do they need to
save?
Answers
Answer:
its b
Step-by-step explanation: