SOLVE CONVERGENCE PROBLEMS ASP

Question

#2 Which of the following series is convergent choice 1, choice 2, choice 3, choice 1 & 2, all choices: (WAITING)

1) 1 is the lower limit ∞ is the upper limit function is (8^n)/(n!),   

 2) 1 is the lower limit ∞ is the upper limit function is (n!)/(n^100), 

 3) 1 is the lower limit ∞ is the upper limit function is (n+1)/(n)(n+2)(n+3)      

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#1 Which of the following series are conditionally convergent? Choice 1 only, choice 1 and 2 only, choice 1 and 3 only, and choice 2 and 3 only

1) 1 is the lower limit ∞ is the upper limit function is (-1^n)/(n) 

 2) 1 is the lower limit ∞ is the upper limit function is ((-1)^n)/(n^3)

 3) 1 is the lower limit ∞ is the upper limit function is ((-1)^n)/(square root of n)

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Answer 1

For #1: 1 and 3 would be conditionally convergent as if they weren't alternating series they would fail the p-series test (exponents of the denominator N term are less than one).

For #2: You would have to preform ratio test on all the series