test the series for convergence or divergence. [infinity] ∑ sin(9n) / 1+9^n n=1

Answers

Answer 1

Answer:

Converges by Direct Comparison Test

Step-by-step explanation:

For the infinite series [tex]\displaystyle \sum^\infty_{n=1}\frac{\sin(9n)}{1+9^n}[/tex], we can use the direct comparison test. We need to check for absolute convergence, so let's assume [tex]\displaystyle \sum^\infty_{n=1}\biggr|\frac{\sin(9n)}{1+9^n}\biggr|\leq\sum^\infty_{n=1}\frac{1}{1+9^n}[/tex].  Since [tex]\displaystyle \sum^\infty_{n=1}\frac{1}{9^n}[/tex] is a geometric series with [tex]\displaystyle r=\frac{1}{9} < 1[/tex], then that series converges. This implies that [tex]\displaystyle \sum^\infty_{n=1}\frac{1}{1+9^n}[/tex] converges, and so [tex]\displaystyle \sum^\infty_{n=1}\frac{\sin(9n)}{1+9^n}[/tex] converges by the direct comparison test.


Related Questions

how do you round to the nearest 10,000 in 1,995,298?

Answers

Answer:

The answer is 2,000,000

Step-by-step explanation:

^^^^^ look up !!!hahhahaha

Help me pleaseeeeeee

Answers

Answer:

1(top)- the last one

2- the first one

3(bottom)- the middle one

Step-by-step explanation:

trust me :)

Find the solution of y = -x - 3 for x = -2.


A.
(-2, 1)


B.
(-2, -5)


C.
(-2, -1)

Answers

Answer:

(-2,-1)

Step-by-step explanation:

y = -x - 3

you replace the x with the -2

y = -(-2) - 3

y=2-3

y=-1

please help me if you can

Answers

X= 35

How to:
Cross Multiply

Answer:

[tex]x=35[/tex]

Step-by-step explanation:

it says what to do in the problem :)

Answers

Answer:

Step-by-step explanation:

1). (10x - 27)° = (2x + 29)°

10x - 27 = 2x + 29

8x = 56

x = 7

m∠W = (2(7) + 29)° = 43°

2). (14x + 4)° + 51° + 55° = 180°

14x + 110 = 180

x = 14

15% is to be added to a 120 pair of shoes. Find the total
Price for the pair of shoes​

Answers

Answer:

138

Step-by-step explanation:

120 x .15 = 18

120 + 18 = 138

Answer:

         138

Step-by-step explanation:

[tex]120+15\%\times120=120+0.15\times120=120+18=138[/tex]

What is the answer to 2/6 + 1/2?

Answers

Answer: hey, there

your answer is 5/6

Step-by-step explanation:

=

2

6

+

1

2

=

1

3

+

1

2

=

2

6

+

3

6

=

2+3

6

Answer:

5/6

Step-by-step explanation:

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(2/6, 1/2) = 6

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(26×11)+(12×33)=?

Complete the multiplication and the equation becomes

26+36=?

The two fractions now have like denominators so you can add the numerators.

Then:

2+36=56

This fraction cannot be reduced.

Therefore:

26+12=56

Solution by Formulas

Apply the fractions formula for addition, to

26+12

and solve

(2×2)+(1×6)6×2

=4+612

=1012

Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(10,12) = 2

10÷212÷2=56

Therefore:

2/6+1/2=5/6

(hope this helps can i plz have brainlist :D hehe)

Ok so like last like night like I was like playing and like when I was like done playing I went to my room and like when I like went to my room I like 额我真的 and like it was like like so like crazy that I almost like died laughing

Answers

Answer: DUDE U GOT SO MANY "LIKE" IN ONE SENTENCE

Step-by-step explanation:

Answer:

like So like um.... like hit like the like heart like button like?

Step-by-step explanation:

i d k :/

Select the correct answer.
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
ОА
Ax = (x+6)(x-4)
OB.
Ay) = (x-6)(x + 4)
Oc.
Ax = (x + 6/(x+4)
OD. Ax) = (x-6)(x-4)

Answers

A is the answer hope i helped goodbye have an amazing day. stop say ain’t it’s income

Answer:

A

Step-by-step explanation:

How are exponents used for measuring an earthquake? Can you explain?

Answers

Answer:

Richter, the Richter scale was used for many years to describe the energy released by an earthquake. ... To estimate the Richter scale measure, write the amplitude, in mm, as 10 raised to an exponent (10x), then add 3 to the exponent, x. For example, if the amplitude is 100 mm, rewrite 100 as 102.

Step-by-step explanation:

4/5+ 1/3 how much is it

Answers

4/5 = 12/15
1/3 = 5/15
17/15 = 1 2/15

The number of students enrolled at a college is 17,000 and grows 6% each year.

Answers

Answer:

1020 new students per year.

Step-by-step explanation:

pls Help!.. help help help

Answers

uhh there’s no picture it just only shows up black when i press it:/

0.86 write the decimal as a fraction in simplest form​

Answers

Answer:

43/50

Step-by-step explanation:

should be right.

Answer:

43/50

Step-by-step explanation:

86/100 divided by 2

I need this ASAP Joe needs at least $75 to take his mom
out for her birthday. So far he has
saved $30. He has 3 days to make the
money. Suppose he earns the same amount each
day,
write
an inequality to find out how much
he needs to earn each day. solve the inequality

Answers

Answer:

He will need to get 15$ a day

Step-by-step explanation:

So what u can do is subtract 30 from 75 u will get 45 divide that by 3 and u get 15. Hope it helps

Direction: Simplify each expression using Product Rule.

: (−
3)(23
) = −2(
3+1
1+3
)

= −2



1. (
2
)(
4
) = 6. (34
)(2
)(
3
)

2. (6
2
)(6
3
) = 7. (−6
2)(−3
3
5
)

3. (
2
)(
4
)(
2
) = 8. (2
2
)(3
4
)

4. (
1
2) (
1
2) = 9. (
1
3) (
2
3) =

5. (
3
5) (
1
5) = 10. (2
1
6) (−3
1
6)=

Answers

Answer:

pagal answer toone khoo

Please I need help ASAP

Answers

Answer:

6, -4

Step-by-step explanation:

Not sure if correct but that's what I got

Which ratio forms a proportiona with 5:15?

A: 10:20
B: 75:5
C: 3:1
D: 1:3

Answers

Answer:

C

Step-by-step explanation:

Answer:

Answer is D.1:3

Step-by-step explanation:

I hope it's helpful!

help please will give brainliest ​

Answers

Answer:

R=0.25

Step-by-step explanation:

Y=RX

2=R×8

2/8=8R/8

R=0.25

The ratio of 15 days to a week is​

Answers

Answer :

The ratio of 15 days to a week is 15 : 7.

[tex] \\ [/tex]

Explanation :

Ratio of 15 days to a week :

[tex] \sf : \implies 15 \: days : 1 \: week = \dfrac{15 \: days}{1 \: week}[/tex]

[tex] \\ [/tex]

Now, we know that 1 week has 7 days.

[tex] \sf : \implies 15 \: days : 1 \: week = \dfrac{15 \: \cancel{days}}{7 \: \cancel{days}}[/tex]

[tex] \sf : \implies 15 \: days : 1 \: week = \dfrac{15}{7}[/tex]

[tex] \sf : \implies 15 \: days : 1 \: week = 15 : 7[/tex]

[tex] \\ [/tex]

Hence, The ratio of 15 days to a week is 15 : 7.

Help me please Thanks

Answers

a) y=x !!!!!!!!!!!!!!!

PLS HELP ASAP I MEAN ASAP PLS

Answers

Answer:

(B). - 3 ≤ x < 1

Step-by-step explanation:

[tex]\frac{\sqrt{x+3} }{\sqrt{1-x} }[/tex]

Given expression is defined for

1). x + 3 ≥ 0 ⇒ x ≥ - 3

and

2). 1 - x > 0 ⇒ x < 1

- 3 ≤ x < 1

A florist used the equation Y=KX to determine how many flowers she'd need for 7 bouquets. She determined she'd need 175 flowers. How many flowers were in each bouquet?

Answers

Answer:

25

Step-by-step explanation:

because 175/7= 25

A city cat show is underway. Complete with purring, meowing, and an occasional hiss. There are three times as many orange cats as black and white cats, two times as many black and white cats as grey cats, three fewer gray cats then white cats, three times as many white cats as calico cats, and five white cats. How many of each kind of cat is in the show? How many in all?

Answers

Answer:

i like cats uwu

Step-by-step explanation:

-4 + x + 7 + 3x + 6x​

Answers

Go to m-a-t-h-w-a-y they give you the answer. But only do it when absolutely necessary. Hope this helps!

Translations, reflections and rotations are all known as

Answers

transformations

hope it helps you

Can you solve 1 and 2 please

Answers

1 A 2 C
Bjigbsnakensndbdbd

Abby needs 8 quarts of milk to make milkshakes for her class party. What would the equivalent amount of milk be in gallons

Answers

Answer:

2 gallons

Step-by-step explanation:

There are 4 (US) quarts in 1 (US) gallon.

Therefore, 2 gallons would equal 8 quarts.

4 + 4 = 8

Answer:

2, 2 gallons would be equal to 8 quarts

Step-by-step explanation:

4 quarts is a gallon so you would have 2

2b - 19 = 11
Show explanation

Answers

Answer:

2b=11+19

2b=30

b=15

heyyyyyyyy guys

2b-19 = 11

+19 on each side

2b = 30

÷2 on each side so b is by itself

b=15

hope that helped^^

Select the correct answer from the drop-Cown menu.
The roots of the quadratic equation
are x= 2 + i.
Drop down options
x^2-4x-5=0
x^2+4x+5=0
x^2-4x+5=0
x^2+4x-5=0

Answers

Answer: Option 3 is correct
Hope this helps : )

The x=2+i is the root of the quadratic equation x²-4x-5=0. Therefore, option A is the correct answer.

What is the solution of a quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, the roots of the quadratic equation are x= 2 + i.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

A) x²-4x-5=0

Here, x=[4±√(16-20)]/2

x=[4±2i]/2

x=2±i

x=2+i or x=2-i

Therefore, option A is the correct answer.

To learn more about the solution of quadratic equation visit:

https://brainly.com/question/18305483.

#SPJ7

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