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Answer:

1

Inconclusive

Step-by-step explanation:

aₙ = (-1)ⁿ / (n + 6)

aₙ₊₁ = (-1)ⁿ⁺¹ / (n + 1 + 6)

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 1 + 6)] / [(-1)ⁿ / (n + 6)]│

lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 7)] × [(n + 6) / (-1)ⁿ]│

lim(n→∞)│[(-1)ⁿ⁺¹ / (-1)ⁿ] × [(n + 6) / (n + 7)]│

lim(n→∞)│-1 × [(n + 6) / (n + 7)]│

lim(n→∞) [(n + 6) / (n + 7)]

1

The limit equals 1, so the ratio test is inconclusive.

Rewrite the factorial parts of the summand as

[tex]\dfrac{(2n+1)!}{n!(n+2)!} = \dfrac{(2n+1)(2n!)}{(n+2)(n+1)(n!)^2} = \dfrac{2n+1}{(n+2)(n+1)} \dbinom{2n}n[/tex]

where [tex]\binom nk[/tex] is the binomial coefficient, and [tex]\binom{2n}n[/tex] are the so-called central binomial coefficients.

Expand the rational expression into partial fractions:

[tex]\dfrac{2n+1}{(n+2)(n+1)} = \dfrac3{n+2} - \dfrac1{n+1}[/tex]

Pull out a constant factor and collect the exponential terms.

[tex]\dfrac{(-1)^{n+1}}{4^{2n+3}} = -\dfrac1{64} \left(-\dfrac1{16}\right)^n[/tex]

The sum we want is now

[tex]\displaystyle \frac{13}8 - \frac1{64} \sum_{n=0}^\infty \binom{2n}n \left(\frac3{n+2} - \frac1{n+1}\right) \left(-\frac1{16}\right)^n[/tex]

Let f(x) and g(x) be functions with power series expansions

[tex]\displaystyle f(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+1}[/tex]

[tex]\displaystyle g(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+2}[/tex]

and recall the well-known binomial series

[tex]\displaystyle \dfrac1{\sqrt{1-4x}} = \sum_{n=0}^\infty \binom{2n}n x^n[/tex]

which converges for |x| < 1/4.

Integrating both sides yields

[tex]\displaystyle \int \frac{dx}{\sqrt{1-4x}} = \int \sum_{n=0}^\infty \binom{2n}n x^n \, dx[/tex]

[tex]\displaystyle -\frac12 \sqrt{1-4x} = C_1 + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+1}}{n+1}[/tex]

Taking x = 0 on both sides, it follows that C₁ = -1/2. We then see that

[tex]\displaystyle f(x) = \frac{1-\sqrt{1-4x}}{2x}[/tex]

Step back and multiply both sides of the binomial series identity by x, then integrate. This yields

[tex]\displaystyle \int \frac x{\sqrt{1-4x}} \, dx = \int \sum_{n=0}^\infty \binom{2n}n x^{n+1} \, dx[/tex]

[tex]\displaystyle -\frac1{12} \sqrt{1-4x} (1 + 2x) = C_2 + C_1 x + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+2}}{n+2}[/tex]

Taking x = 0 again points to C₂ = -1/12. Hence

[tex]\displaystyle g(x) = \frac{1 - \sqrt{1-4x}(1+2x)}{12x^2}[/tex]

Then the value of the sum we want is

[tex]\displaystyle \frac{13}8 - \frac1{64} \left(3g\left(-\frac1{16}\right) - f\left(\frac1{16}\right)\right) = \frac{1+\sqrt5}2 = \boxed{\phi}[/tex]

where ɸ ≈ 1.618 is the golden ratio.

Answer:

3-4 inch= 2.8feet

11/4 = 2.75

2.8-2.75=0.05

Elijsh=2.8

lorie= 2.85

Answer:

(y-84) (y+78

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use below compound interest formula and the given data.

F- future amount, P- invested amount, r - interest rate, n - number of compounds, t- time

Given:

Find the amount after 3 years:

Answer:

C

Step-by-step explanation:

Hello!

In the equation y=a cos bx, we can learn alot about the cosine graph.

a is the amplitude, or how 'long' the cosine graph is.

b is the period, which is how 'wide' one cycle of a cosine period can be. The higher the period, the wider the cycle is.

In this equation, we are focused on finding the period; so any choices that contain amplitude is not a correct answer choice for this problem, which leaves out B and C.

To find the period, we can plug b into [tex]\frac{2\pi }{b}[/tex] , which in a way converts the b value to a period.

For B) y= cos3x

[tex]\frac{2\pi }{3}[/tex]= it does not equal 3 [tex]\pi[/tex]

For C) y=cos [tex]\frac{2}{3}[/tex]x

[tex]\frac{2\pi }{\frac{2}{3}}[/tex]= equals 3 [tex]\pi[/tex] when simplified

Since C equals 3 [tex]\pi[/tex] as a period, C is the only logical answer.

Answer:

6x+9

Step-by-step explanation:

3 x 2x =6x

3x3=9

=6x+9

Answer:

ans is 6x+9

Step-by-step explanation:

3 (2x+3)

=6x+9

7/16 - 7/12 ?

common multiple of 16 and 12 = 48   ((3x16 and 12x4)

7/16 - 7/12 = (7x3) / (16x3) - (7x4) / (12x4) = 21/48 - 28/48 = - 7/48

Answer:

The pattern goes by adding -3.

Using the arithmetic sequence, you can find the 22nd term.

[tex]t_{22} = -2+(22-1)(-3)\\t_{22} = -2+21*-3\\t_{22} = -2-63\\t_{22} = -65[/tex]

Answer:

–2x2 + 13

Step-by-step explanation:

( f o g)(x) = f (g(x))

   = f (–x2 + 5)

   = 2(             ) + 3     ... setting up to insert the input formula

   = 2(–x2 + 5) + 3

   = –2x2 + 10 + 3

Ese mes se le dedujeron $4774, y cobró un sueldo de $19,092.

Dado que el empleado de una compañía tiene un sueldo mensual de L. 23, 865,00, y en el mes de marzo del 2019 se le hizo una rebaja del 20% por llegadas tarde al trabajo, para determinar cuánto se le dedujo y qué sueldo neto sacó ese mes se debe realizar el siguiente cálculo:

Por lo tanto, ese mes se le dedujeron $4774, y cobró un sueldo de $19,092.

Aprende más acerca de cálculos de cantidades en https://brainly.com/question/14342345

Answer:

I belive the correct answers are 8 and 12

Step-by-step explanation:

Answer:

○ -1

Step-by-step explanation:

Looking closely at this piecewise function, when the line on the left-hand side intersects at -3 = y, x is -1.

i hope this work for you

Answer:

38

Step-by-step explanation:

3+8=11

11<38

Answer:

y = -3/2x + 9

Step-by-step explanation:

y = mx + b

y = -3/2x + 9

Answer:

=3

Step-by-step explanation:

Step-by-step explanation:

x = number of minutes

the cost function (in c) of the phone company is

cp(x) = 12x

and the cost function of the discount company is

cd(x) = x/2 + 4600 (R46)

we now need to calculate for what x this becomes the same cost :

12x = x/2 + 4600

24x = x + 9200

23x = 9200

x = 400 minutes

she would have to talk for at least 400 minutes long distance per month to make it an even or then better deal.

with 400 minutes being the break-even point.

so, to make it a better deal (not just equal), she has to talk for at least 401 minutes per month.

Answers:

A. y = -2x + 11

B. y = 1/2x + 5

C. y = -1/2x + 5

D. y = -1/2x + 5

E. y = 2x + 2

F. y = -1/2x + 11/2

Hope this helped! (brainliest please)

Answer:

12

Step-by-step explanation:

(10x - 20) + (6x + 8) = 180

16x - 12 = 180

16x = 192

x= 12

Hi there!

This is an example of supplementary angles, angles that sum up to 180° (they form a straight line).

Summing these two angles up equals 180°, so:

180° = (10x - 20)° + (6x + 8)°

We can drop the ° sign for ease of solving.

180 = 10x - 20 + 6x + 8

Combine like terms:

180 = (10x + 6x) - (20 + 8)

180 = 16x - 12

Add 12 to both sides:

192 = 16x

Divide both sides by 16:

192/16 = 16x/16

x = 12°

Answer:

9 inches

Step-by-step explanation:

Answer:

602 r. 2

Step-by-step explanation:

Answer:

The statement is false.

Answer:

the correct answer should be 500,000 hope this helps

4000 is 0.8% of 500000.

Answer:

-4

Step-by-step explanation:

P(4)= 4^2 - (5*4)

      = 16 - 20

      = -4

Answer:

  8

Step-by-step explanation:

The distance can be found by subtracting the left number from the right number:

  (3 3/8) -(-4 5/8) = (3 3/8) +(4 5/8)

  = (3 +4) +(3/8 +5/8) = 7 + 8/8

  = 8

The distance between the points is 8 units.

15 is the value of the missing side of the right-angled triangle.

An isosceles triangle, which consists of a pair of sides as well as sides with angles identically, is additionally recognized as a right triangle. Two 45° angles and a 90° angle make up a right isosceles triangle. The triangle's three sides add up to 180 degrees in total.

The information that is provided is with respect to the right triangle:

Side 1 is given as = 9

Side 1 is given as = 12

Applying the Pythagoras theorem:

[tex]H^{2} = S1^{2} + S2^{2} \\= 9^{2} + 12^{2} \\\\= 81 + 144\\=225\\h = \sqrt{225} \\h = 15[/tex]

Learn more about right-angle triangles, here:

https://brainly.com/question/3772264

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Work Shown:

[tex]\displaystyle S_n = \sum_{k=1}^{n} \frac{1}{k}\\\\\\\displaystyle S_4 = \sum_{k=1}^{4} \frac{1}{k}\\\\\\\displaystyle S_4 = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\\\\\\\displaystyle S_4 = \frac{12}{12}+\frac{6}{12}+\frac{4}{12}+\frac{3}{12}\\\\\\\displaystyle S_4 = \frac{12+6+4+3}{12}\\\\\\\displaystyle S_4 = \frac{25}{12}\\\\[/tex]

Note: in step 3, I'm adding terms in the form 1/k where k ranges from k = 1 to k = 4 (k being an integer)

Answer:

1020 m

Step-by-step explanation:

340 x 3 = 1020

Answer:

6800

Step-by-step explanation: