Covers and Convergent Series

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  This continues and we have an infinite series for the distance run. 100 + 100(1/10) + 100(1/100) +...+ 100(1/10^n) +... This is a convergent geometric series with a=100 and r=1/10.

• convergence or divergence

  Hence the series ∑▒b_n is not convergent. a_n sin⁡n Clearly and . Hence the series ∑▒b_n is convergent. a_n/((1+|a_n |)) Clearly . Hence the series ∑▒b_n is convergent.

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  Hence the given series is convergent. We have . Hence we have . And the series is convergent. Hence the given series is convergent. 5 / ( a, c, d, f) We have Consider the series . We have .

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  The series is convergent and the sum is: 13) It is a geometric series with a = -2 and r = -5/4.

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• Show that multiplication of an absolutely convergent series and bounded series is convergent.

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