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Algebra2D

Sequences and Series - Theory & Concepts - Series Convergence

Arithmetic and geometric progressions, infinite series, summation notation, and the binomial theorem.

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Infinite Geometric Series Convergence Lab

Series Equation
S∞=∑n=1∞2(0.50)n−1S_\infty = \sum_{n=1}^\infty 2(0.50)^{n-1}
Converges! (|r| < 1)
S∞=a1−r=21−0.50=4.00S_\infty = \frac{a}{1 - r} = \frac{2}{1 - 0.50} = 4.00
Partial Sums Progression S_N (N = 1 to 10)
Limit: 4.00
2.00
1
3.00
2
3.50
3
3.75
4
3.88
5
3.94
6
3.97
7
3.98
8
3.99
9
4.00
10
Partial Sum S_104.00
Infinite Sum S_∞4.00

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