Calculus 2 - Series

Math 2414 Series Project DUE: ____________________________________ Show work, in order, on separate pages – Work in Groups.

1. 1.01 1

1

k k





 2. 1

2 k

k k





 3. 1

0

( 1)

2 1

k

k k







 

4. 3 2 1

( 1) k

k k





  5.

1

! k

k

k

k







6. Find the sum of the series 6 4 8

3

16

9

32

27       .

Find the interval and radius of convergence for the following series:

7. 1 0 3

k

k k

k x



 

 8. 1

10 ( 1)

!

k k

k

x k





 9. 1 4

k

k k

x

k







10. 0

!( 5) k

k

k x 



 11. 2

0 2

k

k k

k x







12. Construct the Taylor series expansion for 2

( ) x

f x e , about 0x  .

13. Construct the Taylor series expansion for ( ) sin( )f x x , about 3

2 x

 

14. From the list of basic power series,       ln( )1 2 3 4

2 3 4

x x x x x

.

A. Use this to create/write a power series for the function  ln( )1 x

x find domain

B. Use the result from part A to find the general term of the power series expression

for the definite integral ln(1 )x

dx x

   and find the domain