(25 points) Determine if each series is convergent or divergent. Clearly state which test(s) you are using, verify that this(these) test(s) is(are) valid (if applicable), and give justification for...

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(25 points) Determine if each series is convergent or divergent. Clearly state which test(s) you are using, verify that this(these) test(s) is(are) valid (if applicable), and give justification for your conclusion. (a) (4 points) X∞ n=2 n n+1 lnn n (b) (5 points) X∞ n=1 1 (n + 1) ln(n + 1) (c) (4 points) X∞ n=1 1 2n + √ n (d) (4 points) X∞ n=2 1 (nlnn) 2 (e) (4 points) X∞ n=0 (n!)3 (3n)! (f) (4 points) X∞ n=1 n n 3 1996+7n 4. (12 points) Find the radius and interval of convergence of the power series. Determine when the series is convergent absolutely or conditionally, and divergent. X∞ n=0 2 n · x n p (4n + 1) · 5 n
Answered Same DayMay 23, 2021

Answer To: (25 points) Determine if each series is convergent or divergent. Clearly state which test(s) you are...

Rajeswari answered on May 24 2021
145 Votes
58708 Assignment
a)
We use ratio test
Let us find ratio of n+1th term to nth term
The term (n+
1) is bigger than n also exponent is larger for numerator
The log term since only log is used will not reduce as fast as the exponent of n increases.
Hence ratio >1 as n tends to infinity. So diverges
b)
This can be done using integral test.
The sum =
Use substitution as ln (n+1) = u
Then we get...
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