i need help with two questions for my calculus about sequences and series

Calculus
Tutor: None Selected Time limit: 1 Day

Apr 26th, 2015

f) The series ∑j=1(–1)j sin j / j3 converges by the comparison test, because |(–1)j sin j / j3| ≤ 1/ j3 and the series ∑j=11/ jp converges for any p > 1. Here p = 3.

g) The series ∑n=21/n(ln n)2 converges since the integral ∫21/x(ln x)2 dx = – 1/ln x ]2= 1/ln 2 converges (note that limx→+∞1/ln x = 0).


Apr 27th, 2015

I noticed that you have also asked about your third question (e) and got a wrong answer. Here is a solution.

Apply the ratio test to the series ∑n=0 [n6n+1 / n!5].

limn→ an+1 /an = limn→∞ [(n+1)6n+2 / (n+1)!5n+1] ÷ [n6n+1 / n!5n] =

limn→∞ [(n+1)·n!·5n·6n+2 / n·(n+1)!·5n+1·6n+1] = limn→∞ 6/(5n) = 0 < 1 and the series converges.



Apr 29th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Apr 26th, 2015
...
Apr 26th, 2015
May 28th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer