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Which geometric series diverges? Three-fifths three-tenths three-twentieths StartFraction 3 Over 40 EndFraction ellipsis Negativ

Sholpan [36]

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

$\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}$

<h3>What is geometric series diverges? </h3>

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

$a+ar+ ar^2+ ar^3+...$

Here,

is the (<em>a</em>) first term of the sequence, and (<em>r</em>) is the common ratio.

To be a series as geometric series diverges, it should follow,

$|r| > 1$

First option given as,

3/5+3/10+3/20+3/40+ ...

Here, the common ratio is,

$r=\dfrac{\dfrac{3}{10}}{\dfrac{3}{5}}\\r=\dfrac{1}{2}$

The common ratio is less than one. Thus option a is not correct.

First option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

$r=\dfrac{4}{-10}\\r=\dfrac{-2}{5}$

For the option number two the common ratio is (-2/5) which is less than 1. This option is also not correct.

In the option number c, the value of common ratio is -4. The absolute value of common ratio is,

$|r|=|-4|\\|r|=4$

The absolute value of this common ratio is more than one. Thus, this is the correct option.

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

$\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}$

Learn more about the geometric sequence here;

brainly.com/question/1509142

7 0

3 years ago

The probability of the spinner landing on the shaded part is p=1/3. The probability of it landing on an unshaded part is q=2/3 t

raketka [301]

Answer:

The correct answer is 0.5.

Step-by-step explanation:

The probability of a spinner landing on the shaded part follows binomial distribution.

Equation to be used is P(r) = $\left[\begin{array}{ccc}n\\r\end{array}\right]$ × $p^{r}$ × $q^{n-r}$ , where n is the number of times the spinner is spun and r is the number of times the spinner falls on the shaded region.

The probability of the spinner landing on the shaded part is p = $\frac{1}{3}$ . The probability of it landing on the unshaded part is q = $\frac{2}{3}$ .

The spinner is spun n = 3 times.

We need to find the probability of it landing on the shaded part r = 2.

∴ Putting the values in the equation gives,

P(r) = $\left[\begin{array}{ccc}3\\2\end{array}\right]$ × $\frac{1}{2} ^{2}$ × $\frac{2}{3} ^{1}$ = 3 × $\frac{2}{3}$ × $\frac{1}{4}$ = 0.5

8 0

3 years ago

Three friends , Jack , DaQuan and Liu go to a restaurant together. When the bill comes , they must determine each persons share.

Afina-wow [57]

8 + 6.50 = 14.50

22.00

- 14.50

-----------

7.50

answer : liu's meal was $7.50

3 0

3 years ago

What is the product of 1 x 10^5 and 6 x 10^3? * 6 x 10^8 3 x 10^15 3 x 10^8 6 x 10^15

Afina-wow [57]

(1 x 10^5) x (6 x 10^3) = (1 x 6) x 10^(5 + 3) = 6 x 10^8

5 0

4 years ago

Read 2 more answers

Administrators at a large public high school are interested in their students’ standardized test scores. Last year, the mean sco

ratelena [41]

Answer:

The appropriate hypotheses for performing a significance test is:

$H_0: \mu = 51$

$H_1: \mu > 51$

Step-by-step explanation:

Last year, the mean score on the state’s math test was 51. The administrators have trained the teachers in a new method of teaching math hoping to raise the scores on this standardized test this year.

At the null hypothesis, we test if the mean score this year is the same as last year, that is:

$H_0: \mu = 51$

At the alternate hypothesis, we test if the mean score improved this year from last, that is:

$H_1: \mu > 51$

The appropriate hypotheses for performing a significance test is:

$H_0: \mu = 51$

$H_1: \mu > 51$

8 0

3 years ago