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3 years ago

100 points to correct answer!!!

Mathematics

1 answer:

Korvikt [17]3 years ago

7 0

Answer:

but u have only provided 5 pts first give 100 pts and I will help u.

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Determine whether the following series converges. Summation from k equals 2 to infinity (negative 1 )Superscript k Baseline Star

Ket [755]

Answer:

$a_k=\left|\dfrac{k^2-3}{k^2+4}\right|;\text{ is nondecreasing for $k>2$}$

$\lim\limits_{k \to \infty} a_k =1$

The series does not converge

Step-by-step explanation:

Given ...

$S=\displaystyle\sum\limits_{k=2}^{\infty}{x_k}\\\\x_k=(-1)^k\cdot\dfrac{k^2-3}{k^2+4}\\\\a_k=|x_k|$

Find

whether S converges.

Solution

The (-1)^k factor has a magnitude of 1, so the magnitude of term k can be written as ...

$\boxed{a_k=1-\dfrac{7}{k^2+4}}$

This is non-decreasing for k>1 (all k-values of interest)

As k gets large, the fraction tends toward zero, so we have ...

$\boxed{\lim\limits_{k\to\infty}{a_k}=1}$

Terms of the sum alternate sign, approaching a difference of 1. The series does not converge.

7 0

3 years ago

Three single-digit numbers multiply to make 168

sleet_krkn [62]

3, 8 and 7 because if you multiply 3 by 8 you get 24 and if you multiply 24 by 7 you
get 168

4 0

3 years ago

Referring to the figure, find the value of x

sergiy2304 [10]

Answer:

x = 93

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x - 73 + x + 67 = 180

2x - 6 = 180 ( add 6 to both sides )

2x = 186 ( divide both sides by 2 )

x = 93

6 0

4 years ago

Read 2 more answers

If a stadium has 15,000 seats sold at $10.00, $12.50, and $15.00 equally distributed in three sections, how much can be made if

madreJ [45]

187500 $ because 5000 seats for each just multiply

6 0

4 years ago

Read 2 more answers

Jessie has a container that contains 18 3/4 cios of ice cream. How many 1/3-cup servings of ice cream are in the container

ladessa [460]

Hi there!

18 × $\frac{3}{4}$ = amount of ice cream in container

13.5 = amount of ice cream in container

Let's replace the number of cups by "C" :

13.5 = C × $\frac{1}{3}$

Isoltate "C" by dividing each side of the equation by $\frac{1}{3}$

40.5 = C

Which means that your answer is : There are 40.5 1/3-cup servings of ice creamin the container!

There you go! I really hope this helped, if there's anything just let me know! :)

7 0

3 years ago