Question
Asked Sep 7, 2019
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Look for the results of the questions below whether they include convergent or divergent series using a relative comparison test (ratio)!

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Expert Answer

Step 1

(a) This is a divergent series.

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Let us say 2+1 2" Therefore, a1 (n+1)2 1 Now, L lim a, = n- a 2"+1 = lim (n 1)2 2" n-co 2(2") lm n 2n1 2" nco 2 lim n n 2n+1 1 2 lim n 2 100 L 2 1, by Rati o Test this series diverges Since, L -

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Step 2

(b)  This is a convergent series.

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Let us say (n1) (2(n1)2"2. (n+1)! (п+1)! n! n! 1 Therefore, a 1 n1 n! 2"+ n- (2n)! 2" 2 2 1 lim a Now, L = n+1 а, 1 lim n 2"+2 2#1 = lim 1 L 2 Since, L 1, by Ratio Test this series converges

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