4. Finding Sums of Infinite Geometric Series
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To calculate the partial sum Sn, add the first n terms.
Partial Sums: S1=2, S2≈2.33, S3≈2.39, S4≈2.40, and S5≈2.40
Graph:
Behavior: Sn appears to approach 512 or 2.4.
n | Calculations | Sn |
---|---|---|
1 | − | 2 |
2 | 2+62 | 614 ≈ 2.33 |
3 | 2+62+362 | 3686 ≈ 2.39 |
4 | 2+62+362+2162 | 216518 ≈ 2.40 |
5 | 2+62+362+2162+12962 | 12963110 ≈ 2.40 |
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