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(Solved): Use the limit comparison test to determine whether \sum_(n=5)^(\infty ) a_(n)=\sum_(n=5)^(\infty ) ( ...
Use the limit comparison test to determine whether \sum_(n=5)^(\infty ) a_(n)=\sum_(n=5)^(\infty ) (2n^(3)-4n^(2)+5)/(3+6n^(4)) converges or diverges.
(a) Choose a series \sum_(n=5)^(\infty ) b_(n) with terms of the form b_(n)=(1)/(n^(p)) and apply the limit comparison test. Write your answer as a fully simplified fraction. For n>=5,
\lim_(n->\infty )(a_(n))/(b_(n))=\lim_(n->\infty )
(b) Evaluate the limit in the previous part. Enter \infty as infinity and -\infty as -infinity. If the limit does not exist, enter DNE.
\lim_(n->\infty )(a_(n))/(b_(n))=
(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive?