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zavuch27 [327]
3 years ago
12

Evaluate the infinite sum

Mathematics
2 answers:
mote1985 [20]3 years ago
8 0

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

Effectus [21]3 years ago
6 0

The sum does not converge because \dfrac76>1.

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Using the normal distribution, we have that:

a) The sketch of the situation is given at the end of this answer.

b) The probability is:

P(2.8 \leq X \leq 7) = 0.8284

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

  • Mean of 4.1 years, thus \mu = 4.1.
  • Standard deviation of 1.3 years, thus \sigma = 1.3.

Item a:

The part between 2.8 and 7 years is shaded on the sketch given at the end of this answer.

Item b:

The probability is the <u>p-value of Z when X = 7 subtracted by the p-value of Z when X = 2.8</u>, thus:

X = 7:

Z = \frac{X - \mu}{\sigma}

Z = \frac{7 - 4.1}{1.3}

Z = 2.23

Z = 2.23 has a p-value of 0.9871.

X = 2.8:

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.8 - 4.1}{1.3}

Z = -1

Z = -1 has a p-value of 0.1587.

0.9871 - 0.1587 = 0.8284, thus:

P(2.8 \leq X \leq 7) = 0.8284

A similar problem is given at brainly.com/question/25151638

7 0
3 years ago
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