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
HELP ME PLEASE!!!!!!!!
garri49 [273]

Perimeter is adding all the outside dimensions. The left side of the shoae is a rectangle, so the bottom line is the same as the top line, 10 feet.


Perimeter = 8 + 10 + 8.9 + 10 + 4 = 40.9 ft.


4 0
3 years ago
Susan needs to simplify the expression shown below.
mash [69]

Answer:

The answer to 75 - ( 8 + 45 ÷ 3 ) × 2= 29

3 0
2 years ago
Please help me ...............
KengaRu [80]

Answer:

b= 7 times the square root of 2

Step-by-step explanation: In a 45-45-90 degree triangle the base and the height both equal x and the hypotenuse is equal to x times the square root of 2.

Hope this helps

5 0
3 years ago
Read 2 more answers
Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt
tino4ka555 [31]

Answer:

The given functions are not same because the domain of both functions are different.

Step-by-step explanation:

The given functions are

f(x)= \sqrt{\dfrac{x+1}{x-1}}

g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}

First find the domain of both functions. Radicand can not be negative.

Domain of f(x):

\dfrac{x+1}{x-1}>0

This is possible if both numerator or denominator are either positive or negative.

Case 1: Both numerator or denominator are positive.

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

Case 2: Both numerator or denominator are negative.

x+1\leq 0\Rightarrow x\leq -1

x-1\leq 0\Rightarrow x\leq 1

So, the function is defined for x≤-1.

From case 1 and 2 the domain of the function f(x) is (-∞,-1]∪[1,∞).

Domain of g(x):

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

So, domain of g(x) is [1,∞).

Therefore, the given functions are not same because the domain of both functions are different.

4 0
3 years ago
A shirt was originally priced at $30. The store is having a 5% off sale. How much will you pay for the shirt after the discount
pishuonlain [190]

Answer:

$28.50

Step-by-step explanation:

multiply 30 by 5 then divide by 100 and subtract the answer by 30

30×5=150

150÷100=1.5

30-1.5=28.50

8 0
3 years ago
Other questions:
  • Solve the system of equations.<br> 4x + y = -3<br> 5x + 3y = 12
    10·1 answer
  • Three thousand four hundred seventy seven ten thousandth standard decimal form
    5·1 answer
  • Solve the equation 3x+5y=16 for y
    14·2 answers
  • A) Area:<br> b) Perimeter:<br> 13 cm<br> add speaker notes
    9·1 answer
  • Hey please help me! :P Giving out brainlest too! :P
    15·1 answer
  • At Brick House Masonry Supply, it is time for annual pay raises for the fork lift operators.
    6·1 answer
  • Fill in the table using the function rules
    11·2 answers
  • At a local pet store guppies are on sell for $0.70 each and sword tails $1.80 each. If amanda buys 4 guppies and 3 sword tails h
    8·2 answers
  • Lady Liberty holds a tablet in her left hand. The tablet is 7.19 m long and 4.14 m wide. If you made a scale drawing using the s
    8·1 answer
  • Parallelogram has 2 pairs of congruent sides and the opposite angles are equal.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!