2(10.8 k+ 2.9) What's the answer

Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

$\sum_{n=1}^{inf}\frac{1}{n^p}$

if p>1 then series converges. In oue case we have:

$\sum_{n=1}^{inf}b_n=\frac{1}{n^4}$

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

5 0

3 years ago

A national study, that revealed a normal distribution, revealed that the average time a student spends studying statistics on a

Neporo4naja [7]

Answer:

Null hypothesis = H0 : μ = 60

Alternative hypothesis = H1 : μ < 60

Step-by-step explanation:

From the question given :

μ = 60 minutes

xbar = 44.27 minutes

s = 20.4 minutes

The alternative hypothesis is the claim ; which is to hypothesize that the average studying time is 44.27 (which is less than the population average studying time)

The null hypothesis is the initial truth and it is the opposite of the alternative hypothesis.

The hypothesis are :

H0 : μ = 60

H1 : μ < 60

5 0

2 years ago

If -6x -7 =7 solve for x

natta225 [31]

Answer:

x=-7/3

Step-by-step explanation:

-6x-7=7

-6x=7+7

x=-14/6

x=-7/3 or in mixed fraction

x=-2 1/3

3 0

3 years ago

Can some one help me with this and explain it?

Tresset [83]

Answer:

A. (3,2)

Step-by-step explanation:

One way to solve without graphing

equate both equations to each other:

$2x - 4 = - x + 5$

add x on both sides:

$2x + x - 4 = 5$

add 4 on both sides:

$2x + x = 5 + 4$

collect like terms:

$3x = 9$

divide 3 on both sides, so

$x = 3$

now that we have x, go back to any one of the equations and substitute x=3 to find y. I'll use y=2x-4

$y = 2x - 4$

sub x=3

$y = 2(3) - 4$

2 × 3 is 6

$y = 6 - 4$

$y = 2$

we now have x and y, so the coordinates are (3,2)

If you want to use the graphing method, substitute in x values of your choice, for example -2 to 2 into each equation to find y and when there is a same coordinate in both equations that is the solution.

y = 2x - 4

when x is -2, y = 2(-2)-4 = -8. (-2,-8)

when x is -1, y = 2(-1) - 4= -6. (-1,-6)

when x is 0, y = 2(0)-4 = -4. (0,-4)

when x is 1, y = 2(1) - 4 = -2. (1,-2)

when x is 2, y = 2(2) - 4 = 0. (2,0)

when x is 3, y = 2(3) - 4 = 2. (3,2)

do the same thing of substituting to the other equation

y = -x + 5

when x is -2, y is 7 (-2,7)

when x is -1, y is 6. (-1,6)

when x is 0, y is 5. (0,5)

when x is 1, y is 4. (1,4)

when x is 2, y is 3. (2,3)

when x is 3, y is 2. (3,2)

plot these coordinates on a graph

they both have same x value (3) and same y value (2)

3 0

2 years ago

The expression (x+10) (x-10) is being simplified below using the FOIL Method. Complete the process by filling in the blanks with

grandymaker [24]

(x + 10(x - 10)
x^2 + 10x - 10x -100
x^2 - 100

a. + (-10x)
b. 0x
c. + (-100)
d. (-100)

8 0

3 years ago