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