What is the value for a?

Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

4 years ago

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Plz help I will mark you brainlist plz help

lakkis [162]

Answer

1.) 50 mistakes per test

2.) 8 girls per group

3.) 27 pages per hour

4.) $1.30 per banana

5.) $0.50 per pencils

6.) 13 points per game

7.) $1.25 per cup of tea

8.) 65 liters per hour

9.) 25 calls per hour

10.) 35 words per minute

11.) 8 miles per liter of gas

12.) 0.4 eggs per day

13.) $28 per hour

14.) 3.5 miles per hour

Step-by-step explanation:

*Hope this helped*

8 0

3 years ago

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A bag with 12 marbles has 3 red marbles and 5 yellow marbles. A marble is chosen from the bag at random. What is the probability

alexgriva [62]

Answer:

3/12 = 1/4

Step-by-step explanation:

There are 12 marbles in the bag. If the marble drawn at random is red, it is one of the 3 red marbles.

The probability is "3 out of 12" = 3/12 which simplifies to 1/4.

7 0

3 years ago

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PLEASE HELPPP!!!!

dybincka [34]

Answer:

A. The point (0,0) shows that the cost is $0 for 0 kg of cashews.

C. The point (2,60) shows that it cost $60 for 2 kg of cashews.

B. The constant of proportionality for this graph is 30.

Step-by-step explanation:

D is wrong

7 0

3 years ago

an iron rod of length 7 upon 8 m was cut into two pieces one piece is 1 upon 7 m long what is the length of the other piece.

bixtya [17]

Answer:

other: $\frac{41}{56}$

Step-by-step explanation:

$\frac{7}{8} =\frac{1}{7} + x\\=> x= \frac{7}{8} - \frac{1}{7} \\=> x= \frac{49}{56} - \frac{8}{56} \\=> x= \frac{41}{56}$

8 0

3 years ago