1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
o-na [289]
3 years ago
7

Use root test to determine the series is convergent/divergent or inconclusive

Mathematics
1 answer:
Alinara [238K]3 years ago
8 0

You can first condense the series to make it simpler to study. If <em>n</em> is odd, then <em>n</em> = 2<em>k</em> - 1, and if <em>n</em> is even, then <em>n</em> = 2<em>k</em> for some <em>k</em> ≥ 1. So for each <em>k</em>, you can pair up the <em>k</em>-th terms of the odd- and even-indexed series.

odd:

\dfrac1{3^{\frac{n+3}2}}=\dfrac1{3^{k+1}}

even:

\dfrac1{3^{\frac n2}}=\dfrac1{3^k}

So the series can be re-indexed as

\displaystyle\sum_{n=1}^\infty a_n=\sum_{k=1}^\infty a_k=\sum_{k=1}^\infty \left(\frac1{3^{k+1}}+\frac1{3^k}\right)=\sum_{k=1}^\infty\frac4{3^{k+1}}

By the root test, the series converges, since

\displaystyle\lim_{k\to\infty}\sqrt[k]{\left|\frac4{3^{k+1}}\right|}=\frac13\lim_{k\to\infty}\left(\frac43\right)^{\frac1k}=\frac13

You might be interested in
1213 students went on a field trip.Seven students traveled in cars and six buses were available.How many students would ride on
Alecsey [184]

Answer:201 students

Step-by-step explanation: Since there are seven kids riding in cars, you would subtract 7 from 1213 to get 1206 students. The six buses means you divide by 6 to get 201 students in each bus.

7 0
3 years ago
An equation of a line perpendicular to the line represented by the equation y = -
dem82 [27]

Answer:

y= 1/2x+1

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
I WILL MARK AS BRAINLIEST!!!!
guapka [62]

Answer:

1. 795, 23

2. 50, she will finish her candy on November 21 so she won't be able to share with her cousins

3. $276, 71 cars

Step-by-step explanation:

1. your equation: y = 35x + 235

plug in 16 to find how many pictures she will have on may 16: y = 35(16) + 235

you get y = 795

for the second part, you know are trying to find how long it will take to get to 1024 pictures, so you know your y, but you don't know your x

your equation: 1024 = 35x + 235

solve to get x = 22.54

this rounds up to 23, so your answer is 23

2. multiply 8 times 4 to get 32

subtract 32 from 82 to fin how many she has left

you get 50

for the second part, divide 82 by 4 to find how many day it will take to finish her candy

you get 20.5

so no, she will not have candy to share with her cousins, and she will finish her candy on November 21

3. for this, you have a negative y intercept since you need to make $24 to start profiting

your equation: y = 6x - 24

plug in 50 to x: y = 6(50) - 24

you get y = 276

so you make $276 with 50 cars

for the second part, plug in 400 to y: 400 = 6x - 24

solve to get x = 70.66

this rounds up to 71, so your answer is 71

3 0
3 years ago
How does 8 x 2 1/3 compare to 8
Temka [501]
<span>D) Greater than 8 because you are multiplying by a number greater than 1.

8 * 2 1/3 = 8 * 7/3 = 56/3 = 18.67
& we know, 18.67 > 8

Hope this helps!</span>
6 0
3 years ago
Read 2 more answers
it costs $5.75 to enter an arcade and $.50 to playing arcade game. You have $7.25. Right in equation that represents the number
Ksju [112]

5.75+3(.50) because it’s 5.75 and then add .50 3 times to get 7.75. Meaning you can play 3 games...

Hope that helps

8 0
3 years ago
Read 2 more answers
Other questions:
  • Calculate the area of the composite figure. which is not a drawn scale.
    14·2 answers
  • Question part points submissions used find an equation of the plane. the plane that passes through the point (−2, 1, 3) and cont
    12·1 answer
  • HELP ASAP PLEASE
    15·2 answers
  • Delaney used one fourth of an ounce of nuts to make a cookie. How many ounces of nuts will she need to make 3 dozen cookies
    12·1 answer
  • How do you do this? show work please.
    11·1 answer
  • A triangle with vertices (-1,1), (2, -1), and (3,0) is translated using the rule x + 2, y - 6). What are the coordinates of the
    9·1 answer
  • (05.01)Elliot has been running a lawn care business since 2000. He cuts grass, trims, and weed whacks yards for his customers th
    9·2 answers
  • 5.) Tiffany is building a model of her bedroom. She is using a scale factor of 1 foot in her room to 0.5 inch in the model. if h
    11·1 answer
  • I need help solving this central angle and trying to find the name and what type of arc it is ​
    11·1 answer
  • Anyone knows this?! ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!