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
pychu [463]
3 years ago
12

(15-16) Consider the Infinite Geometric Series:

Mathematics
1 answer:
vodka [1.7K]3 years ago
5 0

15 Answer:  S₁ = 1       S₂ = 4        S₃ = 13        S₄ = 40       Sum = NO            

<u>Step-by-step explanation:</u>

1 + 3 + 9 + 27 + ...    \implies\sum^{\infty}_{n=1}3^{n-1}\implies\sum^{\infty}_{n=1}\dfrac{3^n}{3}\\\\\bullet S_1=1\\\bullet S_2=1+3=4\\\bullet S_3=1+3+9=13\\\bullet S=1+3+9+27=40\\\\\\ \lim_{n \to \infty} \dfrac{3^n}{3} \implies\dfrac{3^{\infty}}{3}\implies\infty\\\\\text{The series diverges so there is no sum.}

16 Answer:      \bold{S_1=\dfrac{1}{2}\qquad S_2=\dfrac{2}{3}\qquad S_3=\dfrac{13}{18}\qquad S_4=\dfrac{39}{54}\qquad Sum=YES}        

<u>Step-by-step explanation:</u>

\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}+...\implies \sum^{\infty}_{n=1}\dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\\\\\\\bullet S_1=\dfrac{1}{2}\\\\\bullet S_2=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{2}{3}\\\\\bullet S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{13}{18}\\\\\bullet S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=\dfrac{39}{54}

\lim_{n \to \infty} \dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\implies \dfrac{1}{2}\lim_{n \to \infty} \dfrac{1}{3^{\infty-1}}\implies \dfrac{1}{\infty}=0\\\\\\\text{The series converges so it does have a sum.}

You might be interested in
What is 2 and 1 3rd times 5<br>​
DedPeter [7]
2 1/3 = (mixed # x denominator) + numerator/ denominator

= 2x3+1/ 3= 7/3



7/3 x 5= 35/3= 11 2/3



5 0
3 years ago
Read 2 more answers
Find the total surface area of the prism pictured.
marysya [2.9K]

Answer:

choice 2) area = 319.2 in²

Step-by-step explanation:

triangular ends = 6.9 x 8 = 55.2

sides = 3 x 8 x 11 = 264

264 + 55.2 = 319.2 in²

5 0
3 years ago
Help will give brailiest to first answer
siniylev [52]

question isn't loading

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
A city has a population of 210,000 people. Suppose that each year the population grows by 3.25% . What will the population be af
serg [7]

Answer: the population be after 10 years is 289145

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 210000

r = 3.25% = 3.25/100 = 0.0325

t = 10 years

Therefore,

y = 210000(1 + 0.0325)^10

y = 210000(1.0325)^10

y = 289145

5 0
3 years ago
Simplify the expression<br><br> 3.2 - 5.6n - 4n + 8 =
mars1129 [50]

Answer:

maybe 11.2-9.6n...sorry if I get it wrong

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Express each rate as a unit rate
    13·1 answer
  • Unfortunately, the bus broke down at the distance of 50 km continue the story
    12·1 answer
  • Round 3.006 and 3.06 to its nearest tenth
    15·2 answers
  • (01.02 LC) Ben scored in the 85th percentile of his class on the latest math exam. What does this mean in relation to the data s
    10·1 answer
  • SOMEONE PLZ HELP!!<br> Round answer to the nearest hundredth
    6·1 answer
  • Help i need your help with this
    7·2 answers
  • (PLZ ASAP ANSWER !!!!!!)The number line shows the graph of an inequality: A number line is shown from negative 5 to positive 5 w
    11·1 answer
  • In a survey, 250 adults and children were asked whether they know how to
    5·1 answer
  • Year 11 math methods, help pls
    12·1 answer
  • The sum of two polynomials is 8d5 – 3c3d2 5c2d3 – 4cd4 9. if one addend is 2d5 – c3d2 8cd4 1, what is the other addend? 6d5 – 2c
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!