MAT 302 Assignment Problem 9.2

MAT 302 Assignment Problem 9.2 | Borough of Manhattan Community College

9.2 Series and Convergence

Question 1

(1 point) Find the numerical value of the sums below.

Question 2

1 point) Find the numerical value of the sum below.

Question 3

(1 point) Enter a formula for

Question 4

Compute the partial sums S2,S4S2,S4, and S6S6.

Question 5

(1 point)

Compute the partial sums S2,S4S2,S4, and S6S6.

Question 6

(1 point) If sn=∑i=1n(12)i,sn=∑i=1n(12)i, then list the first five terms of the sequence sn.

Question 7

1 point)

Calculate S3,S4S3,S4, and S5S5 and then find the sum for the telescoping series

Question 8

(1 point) Determine the sum of the following series.

Question 9

a) Find a formula for the general term anan (not the partial sum) of the infinite series (starting with a1a1).

a)       

Question 10

(1 point) Find the first five partial sums of the following series. Then find the sum if it is convergent. If it is divergent, type "Diverges" or "D".

∑n=1∞(0.9)n−1

Question 11

(1 point) Find the sum of the following infinite series. If it is divergent, type "Diverges" or "D".

∑n=0∞1(6√)n

Question 12

(1 point) Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent, enter div .
Hint: Use partial fractions to get a telescoping series.

∑n=1∞6n(n+1)

Question 13

If the following series converges, compute its sum. Otherwise, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, and DIV otherwise.

∑n=1∞3+4n4n

Question 14

(1 point) Determine the sum of the following series.

∑n=1∞(3)n−15n

Question 15

(1 point) Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent, enter div .
Hint: Use partial fractions to get a telescoping series.

∑n=1∞7n(n+2)

Question 16

1 point) Determine the sum of the following series.

∑n=1∞(3n+8n12n)

Question 17

(1 point) Find the sum of the convergent series.

∑n=0∞[(0.2)n+(0.5)n]

Question 18

(1 point) Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent, enter div .

∑n=1∞nn+2

Question 19

(1 point) Express the following number as a reduced ratio of integers.

0.52¯¯¯¯¯=0.52525252…

Question 20

(1 point) Express the following number as a ratio of integers.

3.1745¯¯¯¯¯¯¯¯

Question 21

(1 point) Find the values of xx for which the series below converges.

∑n=1∞xn4n

Question 22

(1 point) Consider the following series. Answer the following questions.

∑n=0∞(x+4)n2n

Question 23

(1 point) Consider the following series. Answer the following questions.

∑n=1∞xn4n