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3 years ago

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Mathematics

2 answers:

melamori03 [73]3 years ago

8 0

Answer:

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Step-by-step explanation:

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tatyana61 [14]3 years ago

7 0

Answer:

add 1+1

Step-by-step explanation:

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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:

<u>Given</u> ...

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

whether S converges.

<u>Solution</u>

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

There are three novels on Sam's reading table: Light, Zami, and Money.

ivolga24 [154]

The subsets of the set of novels is given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

<h3>How to find the subsets of a set?</h3>

Suppose we have a set with cardinality n, that is, with n elements. This set will have 2^n subsets, which are all the possible combinations with the elements of the set, including the empty set.

In this problem, the novels are given as follows:

Light, Zami, and Money.

Hence the possible subsets are given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

With is the list that is asked for this problem, which are the subsets of the set of novels.

More can be learned about the sub-sets of a set at brainly.com/question/2000547

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3 0

2 years ago

Fourteen less than the sum of ninety-two and sixty-five

Vsevolod [243]

92+65=157
157-14=143
Answer is 143

hope this helps:)

7 0

3 years ago

Read 2 more answers

Solving 8 problems per Minute, Fast Funn can finish his test in time. He was, however, working fast, solving 10 problems per min

ale4655 [162]

The number of problems that were on the text was 240 problems.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total number of problems that were on the text, y represent the time to be spent, hence:

y = x/8

Also:

y - 6 = x/10

x/8 - 6 = x/10

x = 240

The number of problems that were on the text was 240 problems.

Find out more on equation at: brainly.com/question/13763238

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7 0

2 years ago

Free answers if u want

vladimir2022 [97]

Answer:

Thank you so much!!!

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers