The length of time for one individual to be erved at a cafeteria is a random variable having an ex- ponential distribution with
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I think the given series is
You can use the integral test because the summand is clearly positive and decreasing. Then
Substitute <em>u</em> = <em>x</em> ³ + 1 and d<em>u</em> = 3<em>x</em> ² d<em>x</em>, so the integral becomes
As <em>u</em> approaches infinity, we have ln(<em>u</em>) also approaching infinity (whereas 1/3 ln(9) is finite), so the integral and hence the sum diverges.