Use the Ratio Test to determine whether the series is convergent or divergent. 6 12 18. ... (6n) Σ n! n = 1 Identify an 6. 12· 18 · ... (6n) n! 6- 12· 18· .... (бп) (6n)! (6n)! n! 6n! n! Evaluate the following limit. lim n+ 1 Since lim nt1 1, the series is divergent

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A: According to the ratio test evaluate the value oflimn→∞an+1an   let sn=1n3+a Then   sn=1n+13+a…

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A: Given series:                                    an=∑n=1∞-1n3.6.9 . . . 3n3.7.11 . . .4n-1…

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A: We use the fact that  Lim (1+1/n)n= e

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Q: Consider the two series: 2n + 3 (a) 2 n2 In n n=1 8. 1+ (n – 2)! (b) n! n=1

A: Given series are: ∑n=1∞ 2n+3n2lnn∑n=1∞ 1+n−2!n!

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A: Since you have asked multiple questions but according to our company's guidelines I can only answer…

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