Sn = a (1 – rn)
1 – r
As n→ ∞ and |r| > 1 , |rn|→∞ and Sn →∞
As n→ ∞ and |r| < 1 , |rn|→∞ and Sn →S∞
Therefore,
Sn = a(1 – 0)
1 – r
S∞ = a
1 – r
Example: {4, 2, -1, 0.5, -0.25, 0.125, -0.0625, 0.03125, -0.015625, . . .}.
Solution: a = 4 and r = 0.5
Sn = a
1 – r
4
1 – 0.5
4/0.5
= 8
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