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3 years ago

A rectangular swimming pool measures 16

Mathematics

1 answer:

romanna [79]3 years ago

3 0

Answer:

1344m

Step-by-step explanation:

16x84

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$

note that any constant dividing infinity is equal to zero

$|\frac{1+2/\infty+1/\infty^2}{5}|\\\\$

$\frac{1+0+0}{5}\\ = 1/5$

$\rho = 1/5$

Since The limit of the sequence given is less than 1, hence the series converges.

5 0

2 years ago

A square has the side measurement of s=6^3/2 , Use the formula A = s^2 , find the area of the square

irakobra [83]

$s=6^{ \frac{3}{2} } \\ \\ A=s^2={(6^{ \frac{3}{2} } )}^2=6^{ 3}= 216 \ \ units^2$

7 0

2 years ago

Estimate the product or quotient. 91*17

Diano4ka-milaya [45]

The product is 1800
because 90x20

8 0

3 years ago

The scale of a map is 1:1,000,000. What are the real distances between two points if the distance between them on this map is 35

Inessa [10]

35km; Since the points on the map are one millionth of their actual size, simply multiply by one million and convert from there.

35*1,000,000 = 35,000,000mm

35,000,000/1000 = 35,000m

35,000/1000 = 35km

8 0

3 years ago

Read 2 more answers

Solve the equation 1.5y < -6.75

finlep [7]

1.5y < -6.75

First, divide both sides by '1.5'.
$\frac{-6.5}{1.5}$
Second, since 4.5 × 1.5 = 6.5, simplify the fraction to '-4.5'
$y \ \textless \ -4.5$

Answer: y < -4.5

7 0

2 years ago