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3 years ago

Simple math! i'll mark you if you get it right

Mathematics

1 answer:

miss Akunina [59]3 years ago

4 0

$100 because if you follow the line from 5 hours to the line it lines up with 100 dollars

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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.

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3 years ago

Explain What Happens To The Volume Of A Sphere When

kati45 [8]

A. The volume is 8 times more
b. The volume is 27 times more
c. The volume is 64 times more

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3 years ago

What is the factored form of 8x^24-27^6

gladu [14]

The answer is x^6(2X^6-3)(4X^12+6X^6+9)

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3 years ago

Y = 6 is the equation of a

Olegator [25]

Answer:

vertical line

Step-by-step explanation:

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2 years ago

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In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation o

ehidna [41]

Answer:

(x – h)2 + (y – k)2 = r2

Step-by-step explanation:

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle the equation of the new circle

(x – h)2 + (y – k)2 = r2

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