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
Valentin [98]
3 years ago
10

Consider the infinite geometric series (∞/Σ/n=1) * -4(1/3)^{n-1}.

Mathematics
1 answer:
raketka [301]3 years ago
5 0
The first four terms of the series probably refer to the first four partial sums.

\displaystyle\sum_{n=1}^1-4\left(\frac13\right)^{n-1}=-4\left(\frac13\right)^{1-1}=-4
\displaystyle\sum_{n=1}^2-4\left(\frac13\right)^{n-1}=-\frac{16}3
\displaystyle\sum_{n=1}^3-4\left(\frac13\right)^{n-1}=-\frac{52}9
\displaystyle\sum_{n=1}^4-4\left(\frac13\right)^{n-1}=-\frac{160}{27}

which you can compute either by adding one term at a time, or using the well-known formula,

\displaystyle\sum_{n=1}^kar^{n-1}=a\frac{1-r^{k+1}}{1-r}

(I can provide a link to a derivation I gave in a nearly identical question in the comments)

The series converges as k\to\infty if and only if |r|, which is certainly the case here, since -1.

Extrapolating from the formula above, the sum of the convergent series is

\displaystyle\sum_{n=1}^\infty ar^{n-1}=\frac a{1-r}

so the sum for this series is \dfrac{-4}{1-\frac13}=-6.
You might be interested in
The least common multiple of two numbers is 12. the sum of the two numbers is 10. what are the numbers? ? and ?
igor_vitrenko [27]
Hmm, the  2 numbers are most likely whole numbers
find what adds to 10 and find teh LCM

1 and 9, LCM is 9, nope
2 and 5, LCM is 10, nope
3 and 7, LCM is 21, nope
4 and 6, LCM is 12, yep


the nmbers are 4 and 6
7 0
2 years ago
In ΔSTU, m∠S=(11x+3)∘,∠T=(2x+16)∘, and m∠U=(x+7)∘. Find .
frozen [14]

Answer:

x = 11

Step-by-step explanation:

In ΔSTU ,

m∠S = (11x+3)° ; m∠T = (2x+16)° ; m∠U = (x+7)°

According to angle sum property of a triangle , sum of all the interior angles of the triangle is 180°.

So,

11x + 3 + 2x + 16 + x + 7 = 180

=  > 14x + 26 = 180

=  > 14x = 180 - 26 = 154

=  > x =  \frac{154}{14}  = 11

6 0
2 years ago
Traditionally, the earth's surface has been modeled as a sphere, but the World Geodetic System of 1984 (WGS-84) uses an ellipsoi
sdas [7]

Answer: You are smart, figure it out yourself

Step-by-step explanation:

3 0
2 years ago
-x - y when x = -12 and y =2
kap26 [50]

Answer:

10

Step-by-step explanation:

Negative times a negative is a positive.

so 12-2=10

5 0
3 years ago
Read 2 more answers
50 POINTS
larisa86 [58]

Answer:

see below

Step-by-step explanation:

f(x) = 5x^3 +1, g(x) = – 2x^2, and h(x) = - 4x^2 – 2x +5

f(-8) = 5(-8)^3 +1 = 5 *(-512) +1 =-2560+1 =-2559

g( -6) = -2 ( -6) ^2 = -2 ( 36) = -72

h(9) = -4( 9)^2 -2(9) +5 = -4 ( 81) -18+5 = -324-18+5=-337

3 0
3 years ago
Read 2 more answers
Other questions:
  • Jack earned $972 in 6 years on an investment at a 3% annual simple interest rate. How much was Jack’s investment?
    12·1 answer
  • BRIA is a rectangle. AN=5. NR=x-3. please solve for x, NR, and BI
    9·1 answer
  • You're filling prescriptions in a pharmacy. Your work surface tray gives you an area of 432 square inches to work. If the length
    15·2 answers
  • Best answer gets brainliest!​
    15·1 answer
  • PLEASE HELP ME I ONLY HAVE A FEW MINUTES LEFTTTT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Which of the following are irrational numbers?
    7·2 answers
  • When Connor was 16, he bought his first car. It had 1.67 x 10^5 miles on it. Connor is now 55 and wants to buy his dream car. He
    8·1 answer
  • Hey yall what is 34 x 45 x 567
    10·2 answers
  • Q: Out of 20 attempts a basketball player scored 8 times. What percent of
    14·2 answers
  • I will give brainliest to whoever helps me with this question. Also, if you could please explain to me how you solved it I would
    5·1 answer
  • If one of the acute angles of a right angled triangle is 55 , calculate the remaining angle​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!