5.9.2 For an infinite series:

S_n = a (1 – rⁿ)

1 – r

As n→ ∞ and |r| > 1 , |rn|→∞ and S_n →∞

As n→ ∞ and |r| < 1 , |rn|→∞ and S_n →S∞

Therefore,

S_n = 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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