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In exercise 1, find a defining formula an = f (n) for the sequence.
1.
1 2 22 23 24
1)4,3,2,1,0, 2) , , , , ,
9 12 15 18 21
In exercise 2-6, determine the convergence or divergence of the sequences. If the sequence is convergent, find the limit.
| 2. | |
| (1) an = 1+(1)n | n+1 1(2) an = 12n n |
| 3.sin2(2n+1)(1) an = 2n | cos(2n+3)(2) an = n2 |
| 4.n+(1)n+1(1) an = 2n5. | 2n+1(2) an = 13 n |
| ln(2n+1)(1) an = n | 1(2) an = cos(2 + 2) n |
| 6.(4)n(1) an = n! | 1(2) an = 2+( )2n2 |
- Determine if the geometric series converges or diverges. If the series converges, find
the value.
X (1)n X (3)n
(1) 4n+1 (2) 2n n=1 n=1
- Find a formula for the n-th partial sume of the series and use it to determine if the series converges or diverges. If a series converges, find its value.
3 3 ! X
X
(1) n2 (n+1)2 (2) n+4 n+3 n=1 n=1
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