The three series ∑An,∑Bn, and ∑Cn have the terms An=1/n^8 , Bn=1/n^5 , Cn=1/n. Use the Limit Comparison Test to compare the following series to any of the above series. For each of the series below, you must enter two letters. The first is the letter (A, B, or C) of the series above that it can be legally compared to with the Limit Comparison Test. The second is C if the given series converges, or D if it diverges. So for instance, if you believe the series converges and can be compared with series C above, you would enter CC; or if you believe it diverges and can be compared with series A, you would enter AD.

[infinity]
a. ∑n=1 5n^2+8n^7/ 5n^8 + 6n^3-5

[infinity]
b. ∑n=1 8n^4+ n^2 -8n/ 6n^12 -5n^10 + 8

[infinity]
c. ∑n=1 5n^5+ n^8/ 149n^13+ 6n^5 + 5

Case a) CD

Case b) AC

Case c)  BC

Step-by-step explanation:

Notice that the three series given: A, B and C, are examples of what is referred as "p-series". These type of series are of the form:

which converge if p>1 and diverge otherwise.

Therefore, we know that the series:

 converges since p = 8 in this case

 converges since p = 5 for this case

  diverges since p = 1 (this is the famous "harmonic Series")

Now we study the first series of polymonial quotient

Case a)    

We write both polynomials in numerator and denominator in standard form to compare their leading terms:

Comparing leading terms, we get:

So since it behaves like the harmonic series, we are going to use the Limit Comparison Test with the Harmonic series:

This is a finite and positive number, and therefore, this series for case a) must diverge as the Harmonic series does. As per the requested convention, we write: CD (use series C as comparison and showing that it diverges)

Case b)    

We then compare their leading terms:

So since it behaves like series "A", we are going to use the Limit Comparison Test with the given converging A series:

This is a finite and positive number, and therefore, this series for case b) must converge as series A does. As per the requested convention, we write: AC (use series A as comparison and showing that it converges)

Case c)    

We then compare their leading terms:

So since it behaves like series "B", we are going to use the Limit Comparison Test with the given converging B series:

This is a finite and positive number, and therefore, this series for case c) must converge as series B does. As per the requested convention, we write: BC (use series B as comparison and showing that it converges)

answer: '

the distance between points l and m

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1