CK-12-Calculus

http://www.ck12.org Chapter 8. Infinite Series

5. The series∑∞k= 1 (−^1 k)!k+^1 converges according to the Alternating Series Test. Let∑∞k= 1 (−^1 k)!k+^1 =S. Computes 4
   for∑k∞= 1 (−^1 k)!k+^1 and determine the bound on|s 4 −S|.

The series∑∞k= 1 (−^1 k)k+^1 converges according to the Alternating Series Test. Let∑∞k= 1 (−^1 k)k+^1 =S. Find the least value
ofnsuch that:

6.

∣∣

∣∑nk= 1 (−^1 k)k+^1 −S

∣∣

∣< 0. 05

7.

∣∣

∣∑nk= 1 (−^1 k)k+^1 −S

∣∣

∣<^0.^005

8.

∣∣

∣∑nk= 1 (−^1 k)k+^1 −S

∣∣

∣<^0.^0001

Determine if each series converges absolutely, converges conditionally, or diverges.

9.∑∞k= 1 (− 1 )k+^132 kk

10.∑k∞= 1 (− 21 k 2 )k++ 21 k

11.∑∞k= 1 (− 74 k)k 2 +^1

12.∑∞k= 1 (−^1 k) 72 k+^1

Keywords

1. alternating series


2. alternating harmonic series


3. alternating geometric series


4. alternatingp−series


5. Alternating Series Test


6. Alternating Series Remainder


7. conditional convergence


8. absolute convergence


9. rearrangement