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Technology and Approximation for Series
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Calculus I
CAL1.170 Technology and Approximation for Series
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For S = sum from n=0 to infinity of (-0.8)
n
, a table reports S_12 = 0.599627 and the next term has magnitude 0.8
13
= 0.054976. Required error is at most 0.02. Which explanation is best?
A
Accept S_12, because the next term is less than 0.08 and the signs alternate.
B
Do not accept S_12, because the geometric tail bound is 0.054976/(1 - 0.8) = 0.27488, not below 0.02.
C
Do not accept S_12 because geometric series with negative ratios always diverge.
D
Accept S_12, because negative ratios make the tail exactly zero after an even number of terms.
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