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1 year ago

In which quadrant is the point ( - 2, 3) located?

Mathematics

1 answer:

stepan [7]1 year ago

8 0

ANSWER:

Quadrant ll

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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

Which of the following equations represents a horizontal line through (5,-3)?

Snowcat [4.5K]

X=5 vertical all the best

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2 years ago

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PLEASE HELP!! ASAP!!! There’s another part

xeze [42]

Answer:

??????????

Step-by-step explanation:

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2 years ago

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How do I delete my questions?

pishuonlain [190]

Email them ..they will help you

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2 years ago

Julie and Eric row their boat (at a constant speed) downstream for 40 miles in 4 hours, helped by the current. Rowing at the sam

Liula [17]

Answer: 3 miles per hour

Step-by-step explanation:

Use the formula "distance (d) = rate (r) x time (t)" to create a system of equations.

Let "r" represent the rate they are rowing

Let "c" represent the current

time rate distance EQUATION

Downstream: 4 hours r + c 40 miles 4(r + c) = 40

Upstream: 10 hours r - c 40 miles 10(r - c) = 40

Distribute, then eliminate r to solve for c:

Down: 4r + 4c = 40 → 5(4r + 4c = 40) → 20r + 20c = 200

Up: 10r - 10c = 40 → -2(10r - 10c = 40) → -20r + 20c = -80

40c = 120

÷40 ÷40

c = 3

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2 years ago