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
Mekhanik [1.2K]
2 years ago
15

Which of the following geometric series converges?

Mathematics
1 answer:
Artist 52 [7]2 years ago
8 0

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}

Multiply both sides by <em>r</em> :

rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n

Subtract the latter sum from the first, which eliminates all but the first and last terms:

S_n-rS_n=a-ar^n

Solve for S_n:

(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}

Then as gets arbitrarily large, the term r^n will converge to 0, leaving us with

S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

You might be interested in
What is the answer to this <br>u(2u+5)-4(U+3)​
Yakvenalex [24]

Answer:

its 2u^2-4u+5u-12

Step-by-step explanation:

7 0
3 years ago
PLZ HELP ME WITH THIS I NEED HELP ASAP
ValentinkaMS [17]

Answer:

See below

Step-by-step explanation:

Part A: $125 is constant.

PART B: Earning depends on hour

5 0
3 years ago
Find the distance between the points: (1,2) and (-3,0)
faltersainse [42]
You can create a right angled triangle.
Find the hypotenuse.
The third point of the triangle is (1,0)
using pythagoras, the value of a is 2, b is 3. 2^2 +3^2 = 13.
Therefore the distance between the two points is \sqrt{13}
7 0
2 years ago
Erin and dan went shopping at their local store. Erin bought shirts that cost $12 each and spent $18 on accessories. Dan bought
andrezito [222]

Answer:

2

Step-by-step explanation:

I  think below is your full question:

<em>Erin and Dan went shopping at their local store. Erin bought shirts that cost $12 each and spent $18 on accessories. Dan bought the same number of shirts as Erin for $16 each and spent $10 on accessories. </em>

<em>If Erin and Dan were billed the same amount by the store, how many shirts did each of them buy?</em>

Here is my answer

Let  x is number of shirts

Person             COST              

ERIN                12x+18

DAN                 16x+10

Equally Billed    12x+18=16x+10 <=> x = 2

so each of them buy 2 shirts

7 0
3 years ago
Which number have the same value as 20 tens
fomenos
The answer is 200. 20*10=200
6 0
3 years ago
Read 2 more answers
Other questions:
  • Asphere and a cylinder have the same radius and height. The volume of the cylinder is 64 m3.
    12·1 answer
  • What is the answer and work to this problem. <br> 4x+2y=14<br> 2x+y=7
    9·1 answer
  • Which relation is a function of x?
    5·2 answers
  • The results from spinning a spinner multiple times are given in the table below.
    15·2 answers
  • Which expression is equivalent to the given expression?
    9·1 answer
  • DOES SOMEONE UNDERSTAND???
    7·1 answer
  • I Need Help with my Summer Packet! <br><br>​
    6·2 answers
  • By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one mo
    7·1 answer
  • Which angle is about 30°? ​
    14·1 answer
  • On the library shelf are: -6 mystery books -5 science books -4 history books -3 adventure books Which event gives you a probabil
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!