3 divided by what equals -8.16

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

3 years ago

What is a conversion factor that you can use to convert gallons to pints.How did you find it

swat32

To convert gallons to pints, multiply the gallons by 8. Since there are 4 quarts in a gallon and 2 pints in each quart, you multiply by 8 since 4*2 is 8.

5 0

3 years ago

Read 2 more answers

Write each decimal as a fraction or mixed number in simplest form.<br> 1 3/8

Mnenie [13.5K]

3/2

<em>Step One:</em> 1 3/8, transform the number into a improper fraction:

To have a mixed number in to a improper fraction, you need to use addition and multiplication. For 1 3/8, We first multiply the denominator (8, also know to be the bottom number of the fraction) to the whole number (1). 8x1= 8
NOTE: The original denominator (8) will be use for are improper, again playing as the denominator, we only multiply the denominator for the numerator (which is the top number of a fraction).
After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12
Now we have both numerator and denominator for 1 3/8, we can create the improper fraction. 12 as the numerator and 8 as the denominator. 12/8
We still need to simplify the number. To that, we need the biggest whole number, or rather I call it the lowest number, that can be divide both in 12 and 8.
4 can be divide by both number so: 12/4= 3 and 8/4=2
Now 3 is are simplify numerator and 2 is are simplify denominator.

8 0

2 years ago

Help<br> Please due soon I would really appreciate it

RoseWind [281]

Should be D. Let me know if you need more of an explanation.

7 0

3 years ago

PLEASE HELP I WILL GIVE EXTRA POINTS

Evgen [1.6K]

Answer:

C

Step-by-step explanation:

A relation is a function if each input gives exactly one output. There is one price for each number of pounds, so the relation is a function.

__

<em>Additional comment</em>

Relations expressed in terms of ordered pairs or tables can be identified as "not a function" if any input (x) value is repeated. Relations expressed as a graph will be "not a function" if any vertical line intersects the graph at more than one point. (This is called "the vertical line test.")

The cost function in this case is a straight line through the origin. It has a slope of $5.99/lb. Any polynomial relation will be a function.

6 0

2 years ago