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In: Advanced Math

Create the generating functions in closed form ( not as an infinite sum) using the sequences:...

Create the generating functions in closed form ( not as an infinite sum) using the sequences:

example: 1,1,1,1,1,1,... = 1/(1-x)

1. 0,1,1,1,1,1,...

2. 1,0,0,1,0,0,1,0,0,1,0,0,1,...

3. 0, 0,0,0,1,1,1,1,1,1,1,1,1,...

4. 1, -1, 1, -1, 1,....

5. 1,1,1,0,0,1,1,1,1,1,1,1,1,1,...

6. 0,0,0,1,2,3,4,5,6,..

7. 3,2,4,1,1,1,1,1,...

8. 0,2,0,0,2,0,0,2,0,0,..

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