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3 years ago

Can someone please help me

Mathematics

2 answers:

anzhelika [568]3 years ago

6 0

Answer:

I and II

Step-by-step explanation:

I: 10 is less than or equal to 2(11) - 1

10 <= 22 - 1

10 <= 21

10 is less than or equal to 21

solution

II: 10 is less than or equal to 2(8) - 1

10 <= 16 - 1

10 <= 15

10 is less than or equal to 15

solution

III: 10 is less than or equal to 2(3) - 1

10 <= 6 - 1

10 <= 5

10 is not less than or equal to 5

not a solution

denpristay [2]3 years ago

3 0

I think the answer would be none

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Check the picture below.

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3 years ago

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

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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 =

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

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

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

$\rho = 1/5$

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

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2 years ago

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3 years ago

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Iteru [2.4K]

Answer:

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Step-by-step explanation:

im not fully sure which equation ur looking for but i think thats right lol. hopefully this helps ! :)

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2 years ago

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worty [1.4K]

Answer:

The answer would be 2.9

Step-by-step explanation:

its already rounded

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2 years ago