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sleet_krkn [62]

3 years ago

9

How do you prove that infinite sequences converge? For example how did someone prove that 1 + 1/4 + 1/9 + 1/16 + 1/25 ..... conv

erges to π^2/6. Can someone explain how people do this, and the process to discovering whether or not infinite sequences diverge or converge? An answer fully explaining the process, that is also fairly clear will receive a brainiliest.

1 answer:

dem82 [27]3 years ago

4 0

Answer:Prove that for any nonzero natural

n

it is true that

Sn=1+1/4+1/9+1/16+1/25+1/2<2

I'm sort of at a loss here. I'm not sure if there exists some formula or method to sum this kind of series, since there is a variable ratio…

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Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded? -Above the solid line

baherus [9]

The statement which correctly describes the shaded region for the inequality is $\fbox{\begin\\\ Above the dashed line\\\end{minispace}}$

Further explanation:

In the question it is given that the inequality is $6y-3x>9$ .

The equation corresponding to the inequality $6y-3x>9$ is $6y-3x=9$ .

The equation $6y-3x=9$ represents a line and the inequality $6y-3x>9$ represents the region which lies either above or below the line $6y-3x=9$ .

Transform the equation $6y-3x=9$ in its slope intercept form as $y=mx+c$ , where $m$ represents the slope of the line and $c$ represents the $y$ -intercept.

$y$ -intercept is the point at which the line intersects the $y$ -axis.

In order to convert the equation $6y-3x=9$ in its slope intercept form add $3x$ to equation $6y-3x=9$ .

$6y-3x+3x=9+3x$

$6y=9+3x$

Now, divide the above equation by $6$ .

$\fbox{\begin\\\math{y=\dfrac{x}{2}+\dfrac{1}{2}}\\\end{minispace}}$

Compare the above final equation with the general form of the slope intercept form $\fbox{\begin\\\math{y=mx+c}\\\end{minispace}}$ .

It is observed that the value of $m$ is $\dfrac{1}{2}$ and the value of $c$ is $\dfrac{3}{2}$ .

This implies that the $y$ -intercept of the line is $\dfrac{3}{2}$ so, it can be said that the line passes through the point $\fbox{\begin\\\ \left(0,\dfrac{3}{2}\right)\\\end{minispace}}$ .

To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute $0$ for $y$ in $6y=9+3x$ .

$0=9+3x$

$3x=-9$

$\fbox{\begin\\\math{x=-3}\\\end{minispace}}$

This implies that the line passes through the point $\fbox{\begin\\\ (-3,0)\\\end{minispace}}$ .

Now plot the points $(-3,0)$ and $\left(0,\dfrac{3}{2}\right)$ in the Cartesian plane and join the points to obtain the graph of the line $6y-3x=9$ .

Figure $1$ shows the graph of the equation $6y-3x=9$ .

Now to obtain the region of the inequality $6y-3x>9$ consider any point which lies below the line $6y-3x=9$ .

Consider $(0,0)$ to check if it satisfies the inequality $6y-3x>9$ .

Substitute $x=0$ and $y=0$ in $6y-3x>9$ .

$(6\times0)-(3\times0)>9$

$0>9$

The above result obtain is not true as $0$ is not greater than $9$ so, the point $(0,0)$ does not satisfies the inequality $6y-3x>9$ .

Now consider $(-2,2)$ to check if it satisfies the inequality $6y-3x>9$ .

Substitute $x=-2$ and $y=2$ in the inequality $6y-3x>9$ .

$(6\times2)-(3\times(-2))>9$

$12+6>9$

$18>9$

The result obtain is true as $18$ is greater than $9$ so, the point $(-2,2)$ satisfies the inequality $6y-3x>9$ .

The point $(-2,2)$ lies above the line so, the region for the inequality $6y-3x>9$ is the region above the line $6y-3x=9$ .

The region the for the inequality $6y-3x>9$ does not include the points on the line $6y-3x=9$ because in the given inequality the inequality sign used is $>$ .

Figure $2$ shows the region for the inequality $\fbox{\begin\\\math{6y-3x>9}\\\end{minispace}}$ .

Therefore, the statement which correctly describes the shaded region for the inequality is $\fbox{\begin\\\ Above the dashed line\\\end{minispace}}$

Learn more:

A problem to determine the range of a function brainly.com/question/3852778
A problem to determine the vertex of a curve brainly.com/question/1286775
A problem to convert degree into radians brainly.com/question/3161884

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Linear inequality

Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.

4 0

3 years ago

Read 2 more answers

Determine algebraically whether the function is even, odd, or neither even nor odd.

m_a_m_a [10]

For a function (fn) to be odd:
f(x) = - f(-x)
For a fn to be even:
f(x) = f(-x)
For a fn to be neither even nor odd
f(x) != f(-x) [No Relation]

(-x)^n = x^n for n -> even
(-x)^n = -x^n for n -> odd
In your example:

f(x) = -4x^3 + 4x
f(-x) = -4 (-x)^3 + 4 (-x)^1 ( 3 and 1 are odd powers )
f(-x) = 4x^3 - 4x (take -1 common to do the check)
f(-x) = -( -4x^3 + 4x ) = - f(x) [between the bracket was the original fn]

f(x) = - f(-x)
so the function is odd also called symmetric about the origin

7 0

3 years ago

HELP ME OUTTTTTTTTTTTTTTT

svet-max [94.6K]

Answer:

C (The third one)

Step-by-step explanation:

Light bends when it goes through water

Refracts when hits a specific glass thing

and reflects when it goes off a mirror

3 0

3 years ago

I NEED HELP ASAP!!

zzz [600]

Answer:

C. {-5,-4, -3, 1, 2, 5}

Step by step explanation:

We have been given a graph and we are asked to find the domain of the relation represented in graph.

We can see that our graph is a series of unconnected points. Our function represents integer values. So we can see that our graph represents a discrete function.

Since we know that domain of a discrete function is set of inputs values consisting of only certain values in an interval. .

The set of first value from each of the given points would made domain of our function. Upon looking at our graph we can see that domain of our function is -5,-4, -3, 1, 2 and 5.

Therefore, option C is the correct choice.

7 0

3 years ago

Which is the equation for the line that passes through (3,5) and has a slope of -5

algol [13]

You just have to study more

4 0

3 years ago

Read 2 more answers