1)

2)

3)

4)

5)None of these

Jaeden Frederick
2022-01-24
Answered

Which of the following assertions is true for the given sequences?

1)$\text{Double exponent: use braces to clarify}$ converges

2)$\left\{\frac{n+1}{2n+3}\right\}$ diverges

3)$\{-1+2{(-1)}^{n}\}$ diverges

4)$\left\{n\mathrm{sin}\frac{1}{n}\right\}$ converges

5)None of these

1)

2)

3)

4)

5)None of these

You can still ask an expert for help

Rylee Marshall

Answered 2022-01-25
Author has **6** answers

True sequences:

2)

3)

Now, check convergence of

Apply series Divergence test

=diverges

Thus,

This is a true sequence

3)

Check the convergence of

Apply Divergence test

=diverges

Thus,

asked 2021-02-22

What is the vertex of the quadratic

asked 2021-08-15

A motorboat can maintain a constant speed of 15 mph relative to the water.

The boat makes a trip upstream to a certain point in 15 minutes. the return trip takes 10 minutes.

What is the speed of the current?

The boat makes a trip upstream to a certain point in 15 minutes. the return trip takes 10 minutes.

What is the speed of the current?

asked 2022-06-22

need to find four variables, $\phantom{\rule{thinmathspace}{0ex}}a,\phantom{\rule{thinmathspace}{0ex}}b,\phantom{\rule{thinmathspace}{0ex}}c,\phantom{\rule{thinmathspace}{0ex}}d,\phantom{\rule{thinmathspace}{0ex}}$, and I have four equations:

1) $\phantom{\rule{thickmathspace}{0ex}}{u}_{1}a-{v}_{1}b+c={u}_{1}^{\prime}$

2) $\phantom{\rule{thickmathspace}{0ex}}{u}_{1}b-{v}_{1}a+d={v}_{1}^{\prime}$

3) $\phantom{\rule{thickmathspace}{0ex}}{u}_{2}a-{v}_{2}b+c={u}_{2}^{\prime}$

4) $\phantom{\rule{thickmathspace}{0ex}}{u}_{2}b-{v}_{2}a+d={v}_{2}^{\prime}$

Note that $\phantom{\rule{thinmathspace}{0ex}}{u}_{1},\phantom{\rule{thinmathspace}{0ex}}{v}_{1},\phantom{\rule{thinmathspace}{0ex}}{u}_{1}^{\prime},\phantom{\rule{thinmathspace}{0ex}}{v}_{1}^{\prime},\phantom{\rule{thinmathspace}{0ex}}{u}_{2},\phantom{\rule{thinmathspace}{0ex}}{v}_{2},\phantom{\rule{thinmathspace}{0ex}}{u}_{2}^{\prime},\phantom{\rule{thinmathspace}{0ex}}{v}_{2}^{\prime}\phantom{\rule{thinmathspace}{0ex}}$ are all known.

Any suggestions to how to solve for the four variables, $a,b,c,d$?

1) $\phantom{\rule{thickmathspace}{0ex}}{u}_{1}a-{v}_{1}b+c={u}_{1}^{\prime}$

2) $\phantom{\rule{thickmathspace}{0ex}}{u}_{1}b-{v}_{1}a+d={v}_{1}^{\prime}$

3) $\phantom{\rule{thickmathspace}{0ex}}{u}_{2}a-{v}_{2}b+c={u}_{2}^{\prime}$

4) $\phantom{\rule{thickmathspace}{0ex}}{u}_{2}b-{v}_{2}a+d={v}_{2}^{\prime}$

Note that $\phantom{\rule{thinmathspace}{0ex}}{u}_{1},\phantom{\rule{thinmathspace}{0ex}}{v}_{1},\phantom{\rule{thinmathspace}{0ex}}{u}_{1}^{\prime},\phantom{\rule{thinmathspace}{0ex}}{v}_{1}^{\prime},\phantom{\rule{thinmathspace}{0ex}}{u}_{2},\phantom{\rule{thinmathspace}{0ex}}{v}_{2},\phantom{\rule{thinmathspace}{0ex}}{u}_{2}^{\prime},\phantom{\rule{thinmathspace}{0ex}}{v}_{2}^{\prime}\phantom{\rule{thinmathspace}{0ex}}$ are all known.

Any suggestions to how to solve for the four variables, $a,b,c,d$?

asked 2022-05-29

Is a non-zero integral multiple of an irrational number guaranteed to be irrational?

asked 2022-05-29

For an irrational number

$x=\sum _{n\in \mathbb{Z}}{a}_{n}{10}^{n}$

Does ${a}_{n}$ takes all the numbers between $0$ and $9$ ?

$x=\sum _{n\in \mathbb{Z}}{a}_{n}{10}^{n}$

Does ${a}_{n}$ takes all the numbers between $0$ and $9$ ?

asked 2022-04-19

Solve please

$\frac{{x}^{2}-4}{x-2}=2$

$\frac{x+4}{x-2}=0$

$\frac{x-3}{x+2}\ge 0$

$\frac{x+2}{x+3}<\frac{x-1}{x-2}$

asked 2022-05-28

Let $[1;\overline{2,1}$ be a continued fraction. Find the corresponding number.