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Determine if diverges, converges, or converges conditionally.

TEA [102]

The given series is conditionally convergent. This can be obtained by using alternating series test first and then comparing the series to the harmonic series.

<h3>Determine if diverges, converges, or converges conditionally:</h3>

Initially we need to know what Absolute convergence and Conditional convergence,

If $\sum|a_{n} |$ → converges, and $\sum a_{n}$ → converges, then the series is Absolute convergence

If $\sum|a_{n} |$ → diverges, and $\sum a_{n}$ → converges, then the series is Conditional convergence

First use alternating series test,

$\lim_{k \to \infty} \frac{k^{5} +1}{k^{6}+11 }$ = $\lim_{n \to \infty} \frac{5}{6k}$ = 0,

The series is a positive, decreasing sequence that converges to 0.

Next by comparing the series to harmonic series,

$\sum^{\infty} _{k=2}|(-1)^{k+1} \frac{k^{5} +1}{k^{6}+11 }|=\sum^{\infty} _{k=2}\frac{k^{5} +1}{k^{6}+11 }$ ≈ $\sum^{\infty} _{k=2}\frac{1}{k}$ = 0

This implies that the series is divergent by comparison to the harmonic series.

First we got that the series is converging and then we got the series is divergent. Therefore the series is conditionally convergent.

$\sum|a_{n} |$ → diverges, and $\sum a_{n}$ → converges, then the series is Conditional convergence.

Hence the given series is conditionally convergent.

Learn more about conditionally convergent here:

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7 0

2 years ago

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5+(×-2)=-8 need help with answer

Jet001 [13]

Answer:

5 + x + (-2) = - 8 simplifies to:

x + 3 = - 8

Subtract 3 from both sides to get variables on one side of the equal sign and constants on the other.

x = - 8 - 3

x = - 11

Step-by-step explanation:

7 0

3 years ago

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Your mother has a new cell phone. It comes with 18 applications already installed. She uses only of those applications. She down

agasfer [191]

If she already has 18 apps, which she uses, and downloaded 12 more, then you just add 18+12.

18+12=30

hope it helps! :3

4 0

3 years ago

12. Building codes regulate the steepness of stairs. Homes must have steps that are at least 13 inches wide for each 8 inches

AfilCa [17]

Answer:

Slope tells you about the steepness of a line. It can is the ration of vertical change to horizontal change and you can solve this by using the slope formula:

a. So in your case, starting from the bottom, the slope is:

If you want to use coordinates, you can think of the first point (bottom of the stairs} would be at the point of origin (0,0). The next point would be at the top of the first stair 13 inches wide (horizontal or x) and 8 inches high (vertical or y)

So the coordinates of the two points would be:

(0,0) and (13, 8)

Using the formula we would have:

b. Looking at the answer above, you can see that the slope with increase if the vertical change is greater, so if you increase the height of the stairs, the stair would be steeper. The opposite is true if you would increase the width.

However, if you proportionally increase the width and the height, then the slope will remain the same.

Step-by-step explanation:

7 0

4 years ago

Solve for N? 1/20 = N/300

Lynna [10]

N=15. Equation: You need to isolate N. Multiply both sides by 300 to get 300/20 = N. You can simplify it to 15.

3 0

3 years ago

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