Question

Consider the series ?_{n=1}^{?} a_n = ?_{n=1}^{?} rac{9 + n^5 + 5n^1}{n^3 + n^7}. We want to use the limit comparison test to determine whether this series converges or diverges. (a) The dominant term of the numerator is n^5. The dominant term of the denominator is n^7. We should therefore use b_n = We get c = lim_{n??} | rac{a_n}{b_n} | = (b) Which of the following statement is true for the series ?_{n=1}^{+?} b_n? A. The series diverges by the geometric series test since r = rac{5}{9} > 1 B. The series converges by the geometric series since r = rac{9}{5} < 1 C. The series diverges by the nth term test for convergence. D. The series converges by the p-test since p = 2 > 1. E. The series diverges by the p-test since p = -5 ? 1. F. none of the above (c) What does the limit comparison test tell you about the series rac{9 + n^5 + 5n^1}{2n^3 + n^7} ? A. The series converges B. The series diverges C. The test tells us no information D. none of the above

          Consider the series
?_{n=1}^{?} a_n = ?_{n=1}^{?} rac{9 + n^5 + 5n^1}{n^3 + n^7}.
We want to use the limit comparison test to determine whether this series converges or diverges.

(a) The dominant term of the numerator is n^5.
The dominant term of the denominator is n^7.

We should therefore use b_n = 

We get
c = lim_{n??} | rac{a_n}{b_n} | =

(b) Which of the following statement is true for the series ?_{n=1}^{+?} b_n?

A. The series diverges by the geometric series test since r = rac{5}{9} > 1
B. The series converges by the geometric series since r = rac{9}{5} < 1
C. The series diverges by the nth term test for convergence.
D. The series converges by the p-test since p = 2 > 1.
E. The series diverges by the p-test since p = -5 ? 1.
F. none of the above

(c) What does the limit comparison test tell you about the series rac{9 + n^5 + 5n^1}{2n^3 + n^7} ?

A. The series converges
B. The series diverges
C. The test tells us no information
D. none of the above

Consider the series
?n=1^? an = ?n=1^? rac9 + n^5 + 5n^1n^3 + n^7.
We want to use the limit comparison test to determine whether this series converges or diverges.

(a) The dominant term of the numerator is n^5.
The dominant term of the denominator is n^7.

We should therefore use bn =

We get
c = limn?? | racanbn | =

(b) Which of the following statement is true for the series ?n=1^+? bn?

A. The series diverges by the geometric series test since r = rac59 > 1
B. The series converges by the geometric series since r = rac95 < 1
C. The series diverges by the nth term test for convergence.
D. The series converges by the p-test since p = 2 > 1.
E. The series diverges by the p-test since p = -5 ? 1.
F. none of the above

(c) What does the limit comparison test tell you about the series rac9 + n^5 + 5n^12n^3 + n^7 ?

A. The series converges
B. The series diverges
C. The test tells us no information
D. none of the above

Added by Rebecca H.

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