Question

Let \sum x_n be a series such that $x_n > 0$ for all $n \in \mathbb{N}$. If $\lim_{n \to \infty} \frac{5^n x_n}{2^n} = 0$, then Select one: a. The series \sum x_n is divergent by nth Term Test. b. The series \sum x_n is divergent by Limit Comparison Test. c. Non of them. d. The series \sum x_n is convergent by Limit Comparison Test. e. The series \sum x_n is convergent by nth Term Test.

          Let \sum x_n be a series such that $x_n > 0$ for all $n \in \mathbb{N}$. If $\lim_{n \to \infty} \frac{5^n x_n}{2^n} = 0$, then
Select one:
a.
The series \sum x_n is divergent by nth Term Test.
b.
The series \sum x_n is divergent by Limit Comparison Test.
c. Non of them.
d.
The series \sum x_n is convergent by Limit Comparison Test.
e.
The series \sum x_n is convergent by nth Term Test.

Let ∑xn be a series such that xn > 0 for all n ∈ℕ. If limn →∞(5^n xn)/(2^n) = 0, then
Select one:
a.
The series ∑xn is divergent by nth Term Test.
b.
The series ∑xn is divergent by Limit Comparison Test.
c. Non of them.
d.
The series ∑xn is convergent by Limit Comparison Test.
e.
The series ∑xn is convergent by nth Term Test.

Added by Jenny H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

Let sum x_(n) be a series such that x_(n)>0 for all ninN. If lim_(n->infty )(5^(n)x_(n))/(2^(n))=0, then Select one: a. The series sum x_(n) is divergent by nth Term Test. b. The series sum x_(n) is divergent by Limit Comparison Test. c. Non of them. d. The series sum x_(n) is convergent by Limit Comparison Test. e. The series sum x_(n) is convergent by nth term Test. Let Z xp be a series such that X,> O for all n E N. If lim n 2n =0,then Select one: Oa. The series >' xn is divergent by nth Term Test. The series , is divergent by Limit Comparison Test. O c. Non of them O d. The series x, is convergent by Limit Comparison Test. e The series , is convergent by nth Term Test.