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Math Assignment Help With For An Infinite Series

5.9.2 For an infinite series:

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

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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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