Question
Asked Sep 1, 2019
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23. Choose the series that converges:
2"
b) Σ
(n+1)!
Θ ΣΙ2--]
3
Ο Σ
2
n-1
n=1
n-0
1
d)
ο Σ
n
e)
n=1 n1
n-1
-5
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23. Choose the series that converges: 2" b) Σ (n+1)! Θ ΣΙ2--] 3 Ο Σ 2 n-1 n=1 n-0 1 d) ο Σ n e) n=1 n1 n-1 -5

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Expert Answer

Step 1

a) Here, we find first few partial sum ,since lim sn as n approaches infinity does not exist. Therefore series diverges.

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Σ 2-(-1) n-1 S2 +(-) s,-2+(-) 2+() 42+()3 etc

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Step 2

b)Here, we apply Ratio test, since the limit is less than 1, so ,the series converges

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2"- 2" (n+2)! n (n+1) lim nlim2*1 (n+1)-- lim- (n+2) 2 = 0 n n2 2"2

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Step 3

c). This is a geometric series with common ratio ...

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1 ||

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