If [infinity]∑n=0cn9n is convergent, does it follow that the following series are convergent? (a) [infinity]∑n=0cn(−3)n

Mathematics

1 answer:

Pepsi [2]2 years ago

7 0

Given: The series ∑cₙ $9^n$ is convergent

To find: The series ∑cₙ $(-3)^n$ is convergent or not.

Solution: If the radius of convergence R the we can conclude that R≥4

So, the series will converge as -3<9.

You might be interested in

Josh estimates the height of his desk. What is a reasonable estimate?

Vesna [10]

The reasonable estimates are indicated in the following choices:

A) 1 foot

B) 2 feet

C) 5 feet

D) 9 feet

So, from the given choices, 2 feet or approximately 24 inches would be the most viable answer because most standard desks have a height around 28 inches to 30 inches. 1 foot is too low, while 5 feet and 9 feet are too high. Therefore, 3 to 4 feet would be the most perfect answer but since we have a limited number of options, the nearest reasonable estimate value would be 2 feet. <span>The original numbers from a problem does not exceed in a reasonable estimate.</span>

3 0

2 years ago

I don't have a question but I was wondering if you could check my work

cestrela7 [59]

The mean of a data sample can be found by adding all the terms in the data sample and dividing the result by the number of terms. In the first case we have the following data sample:

$12,8,15,11,9$

The mean of this sample is:

$\operatorname{mean}=\frac{12+8+15+11+9}{5}=\frac{55}{5}=11$

The mean absolute deviation is the sum of the differences between each data value and the mean, divided by the number of data values, the formula is:

$MAD=\frac{\sum ^{}_{}\mleft|x_i-\bar{x}\mright|}{n}$

Therefore, we must calculate the positive difference between each value and the mean, add them up, and divide the result by the number of data points in the sample. In the case of the first sample we get: