Learning Materials
Features
Discover
Chapter 7: Problem 51
Use the Ratio Test to determine the convergence or divergence of the series. $$ \sum_{n=1}^{\infty} \frac{n !}{n 3^{n}} $$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Define a geometric series, state when it converges, and give the formula for the sum of a convergent geometric series.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(\sum_{n=1}^{\infty} a_{n}=L,\) then \(\sum_{n=0}^{\infty} a_{n}=L+a_{0}\).
Consider the sequence \(\left\\{a_{n}\right\\}\) where \(a_{1}=\sqrt{k}, a_{n+1}=\sqrt{k+a_{n}}\), and \(k>0\) (a) Show that \(\left\\{a_{n}\right\\}\) is increasing and bounded. (b) Prove that \(\lim _{n \rightarrow \infty} a_{n}\) exists. (c) Find \(\lim _{n \rightarrow \infty} a_{n}\).
Compute the first six terms of the sequence \(\left\\{a_{n}\right\\}=\\{\sqrt[n]{n}\\} .\) If the sequence converges, find its limit.
(a) write the repeating decimal as a geometric series and (b) write its sum as the ratio of two integers $$ 0.0 \overline{75} $$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine