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

Question

(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 XXXXXXXXXX7n XXXXXXXXXXpoints) 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

Rajeswari · Accepted Answer

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.

(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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