Reference no: EM132848807
Getting Serious About Series
Question 1: Express each of the following series in expanded notation. Include at least six terms.
1. ∑n=1∞ 1/n3
2. ∑n=1∞ 12(-1/2)n
3. ∑n=1∞ (-1)nn/n+2
4. ∑n=1∞ 1/√n
5. ∑n=1∞ 243(2/3)n
6. ∑n=1∞ [sin(2n-1)/2Π].1/n
7. ∑n=1∞ -1n+1 ln.n/n+1
8. ∑n=1∞ 64(3/2)n-1
9. ∑n=1∞ [cos(Πn)]n/n2+1
10. ∑n=1∞ (5/n!)
Question 2: Express each of the following infinite series in sigma notation. (More than one answer may be possible)
11. 16 + 4 + 1 + 1/4 + 1/16 + 1/32 + ......
12. 1/2 + 1/5 + 1/10 + 1/17 + 1/26 + 1/37+ ....
13. -9 + 27 - 81 + 243 - 729 + .....
14. 1 + 1/3√4 + 1/3√9 + 1/3√16 + 1/3√24 + 1/3√36 + ....
15. x2/2 + x4/4 + x6/6 + x8/8 + x10/10 + x12/12+ .....
16. 64 + 48 + 36 + 24 + 81/4 + 243/16 + ......
17. -7 + 7 -7 + 7 -7 + 7 .....
18. 1 + 1/4 +1/9 + 1/16 + 1/25 + 1/36 + ....
19. 1 -1/2 + 1/6 - 1/24 + 1/120 - 1/170 + .....
20. 1 + 1/4√2 + 1/9√3 + 1/32 + 1/25√5 + 1/36√6 + .....
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