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Andrews [41]
3 years ago
10

Find the limit of the sequence of partial sums whose general term is

D%7Bn%21%7D" id="TexFormula1" title="a_n=\frac{100^n}{n!}" alt="a_n=\frac{100^n}{n!}" align="absmiddle" class="latex-formula">
10

1

DNE

0

I am torn between the limit not existing and it being = 0.

Thank you so much.
Mathematics
1 answer:
nasty-shy [4]3 years ago
7 0

Answer:

0

Step-by-step explanation:

If ∑aₙ converges, then lim(n→∞)aₙ = 0.

Using ratio test, we can determine if the series converges:

If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.

If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.

lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) / (100ⁿ / n!)|

lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) × (n! / 100ⁿ)|

lim(n→∞) |(100 / (n+1)|

0 < 1

The series converges.  Therefore, lim(n→∞)aₙ = 0.

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The following table shows the​ weights, in hundreds of​ pounds, for six selected cars. Also shown is the corresponding fuel​ eff
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Answer:

Step-by-step explanation:

Given is a table showing  the​ weights, in hundreds of​ pounds, for six selected cars. Also shown is the corresponding fuel​ efficiency, in miles per gallon​ (mpg), for the car in city driving.

Weight Fuel eff. x^2 xy y^2

X Y    

28 20 784 560 400

3 22 9 66 484

35 19 1225 665 361

32 22 1024 704 484

30 23 900 690 529

29 21 841 609 441

     

Mean 26.16666667 21.16666667 797.1666667 549 449.8333333

     

Variance   112.4722222  1.805555556

Covariance -553.8611111    

     

     

r -0.341120235    

Correlaton coefficient =cov (xy)/S_x S_y

Covariance (x,y) = E(xy)-E(x)E(y)

The correlation coefficient between the weight of a car and the fuel efficiency is -0.341

8 0
3 years ago
Mean median mode range of 13,11,8,8,12,8
igomit [66]
I think the median is 8 or 11
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3 years ago
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there are 192 players in a basketball tournament each player will have 3 family members at each game each team will play at leas
alisha [4.7K]

Answer:

there are in total 192 basketball players and 486 family memebers the least amount would be 243

Step-by-step explanation:

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3 years ago
Before you factor you should check what two things?
Sergeeva-Olga [200]

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Find m\angle Bm∠Bm, angle, B.
Natalija [7]

Answer:

The answer is that the measure of ∠α is ≈ 20° when rounded to the nearest °

Step-by-step explanation:

To find the measure of ∠α you need to use the reciprocal of the formula for the law of sine which says that a/Sinα = b/Sinβ = c/Sin C. The reciprocal of this gives the new equation that states Sinα/a = Sinβ/b = Sin C/c, and this will help you to find the measure of the missing angle in °'s.

In the triangle line segment BC = 5units is opposite to point A & ∠α. Line segment AC = 7units  is opposite of point and ∠β which is = 28°. And finally, the hypotenuse length and the values of point C & ∠C are unknown, so they aren't important to solving the problem. Knowing all this you can plug in all the known values into the new formula, and start working on figuring things out.

To find the measure ∠α, you first write down everything, putting things into their proper places, so since you're solving for sinα you want the equation to look like this:

sinα/5 = sin28°/7

Then for the second step, you want to isolate the sinα. (To get it by itself × both left and righthand sides by 5 to begin simplifying).

This leaves you with :

sinα = sin28°÷7 · (5)    [And allows you to now solve for the right side of the equation, bringing us to our third step which is to once again simplify. So what you want to do is whip out your calculator and set it to degree mode, so you can find the of sin28° which is = 0.46947156278. Then ÷ that by 7, which will get you a number = 0.06706736611. Finally, take 0.06706736611 × 5,  and you will get the value = 0.33533683056, as your final answer in the third step]

Your equation should now look something like this :

sinα = 0.06706736611 × 5 or 0.33533683056

Moving onto the fourth step, you need to use the inverse of the trig function of sin to get your absolute value. (remember the inverse of sine or acrsin = sin^-1) Here you will need to multiply sin^-1 by 0.33533683056.

And also by now, you'll want to stop writing the equation as sinα = sin^-1 ×

0.33533683056, otherwise you won't get an answer, instead, you'll need to write:

α = sin^-1 × 0.33533683056

So once you do that for the fifth and final step, you'll need to simplify the equation on the righthand side one last time, and you should get the answer of α = 19.5930217327°. Which when rounded to the nearest ° is ≈ 20°.

7 0
2 years ago
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