Sequence Convergence 1

Sequences are a lists of values, that can be generated by the use of a formula. You generally see a pattern and then we have to determine if the sequence will converge or approach a finite number or not. For series that do not converge we can see the limit to see what the series approaches.

Examples covered in this series:

1. {An} = {10 + (-1)^n}
2. {An} = {cos(2n Pi)}
3. {Bn} = {5cos(n Pi)}
4. {Cn} = {cos(n Pi) - (-1)^n}
5. {An} = { [(-1)^n] / n^2}
6. {An} = { 3n / 1 - 2n}
7. {An} = {5n^2 / (n^2) +2}
8. {An} = {13n^2/15n}
9. {An} = {5n^2 / (n^2) + 2 }
10. {An} = {5n/ sqrt( n^2 + 4))}
11. {Bn} = { n^2 / 5^n  - 7}
12) The recursive function {Cn} with c1 = 1/3 and Cn+1 = 3Cn
13) The recursive function {An} with A1 = 256, An+1 = Sqrt(An)
14) The sequence with terms {1/1, 2/4, 3/9, 4/16, 5/25, ... }
15) The sequence with terms { 1, 8, 27, 64, 125, 216, ... }
16) The sequence with terms { 1/3, 3/9, 5/27, 7/81, 9/243, ... }
17) The sequence with terms { -3/2 , 3/4, -3/6, 3/8, -3/10, ...}
18) The sequence with terms { 1/4, 2/9, 3/16, 4/25, 5/36, ...}

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