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
Murljashka [212]
3 years ago
5

Write out the first few terms of the series Summation from n equals 0 to infinity (StartFraction 2 Over 3 Superscript n EndFract

ion plus StartFraction (negative 1 )Superscript n Over 5 Superscript n EndFraction ). What is the​ series' sum?
Mathematics
1 answer:
anyanavicka [17]3 years ago
5 0

Answer:

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8

Step-by-step explanation:

The sum you are trying to understand is this.

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}

Remember that in general when you have a geometric series  

\sum\limits_{n = 0}^{\infty} a*r^n you have that

\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}      and that equality is true as long as     |r| < 1.

Therefore here we have

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n        and   \big|\frac{-1}{15} \big| = \frac{1}{15} < 1

Therefore we can use the formula and

\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n =  \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16  = 15/8

You might be interested in
Plz help it’s due tonight!!!
Nutka1998 [239]
D. Is the ans
Please mark me as Brainliest
8 0
2 years ago
How many triangles exist with the given angle measures? 40 25 115
Valentin [98]
B i am pretty sure
<span>Hope this helps!!:)
Have a good day!!:D
Plz mark brainliest!!XD<span>
</span></span>
5 0
3 years ago
Read 2 more answers
Plz help I’ll pay I promise this is timed
Wewaii [24]

Answer:

you can say u are mutiplying them by two each times see

2:16

4:32

6:48

8:64

10:80

12:96

Step-by-step explanation:

mark brainlyest

4 0
3 years ago
Gia is running for school president. Her best friend designed a rectangular button that measures 2.5 inches by 2 inches. Gina li
vaieri [72.5K]

Answer:

B. 1 inch to 2 feet

Step-by-step explanation:

from 2.5 inches by 2 inches to 5 feet by 4 feet

hence.

the scale factor is "<u>2 inche</u>s to <u>4 feet</u>" which is 1 inch to 2 feet

8 0
3 years ago
I need help with this please
Elena-2011 [213]

Answer:

10(5v-6)

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • What is the volume of this container?
    12·2 answers
  • Please helps it’s easy
    9·2 answers
  • Sunshine bank offers 6% simple interest on deposits. Tangerine bank offers 5% interest compound annually. State the difference i
    6·2 answers
  • Use complete sentences to explain why it is not possible to simplify the following trigonometric expression.
    15·2 answers
  • Name three coplanar points
    11·1 answer
  • Slope intercept form of y-3=2/3(x+5)
    5·1 answer
  • What is the value of x?
    9·1 answer
  • Ayudemen porfavor . Determine 4 ala potencia x + 4 ala potencia -x, si se sabe que 2ala potencia x + 2 ala potencia -x =3
    13·1 answer
  • Read the problems and and write the word that indicates an equation or inequality and decide whether an equation or inequality i
    14·1 answer
  • Please answer the question in the picture
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!