Answer to: Test the convergence of the series. Sigma_{n = 1}^{infinity} 1 . 3 . 5 . . . . . (2n - 1) / (n + 1) 3^n n! By signing up, you'll get...
Is the series \sum_{k=1}^{\infty} \frac{\sqrt{k+1}-\sqrt k}{\sqrt k} convergent or divergent? Test the convergence of the series: \sum_{n = 0}^{\infty} \frac{n^3 + 1}{2^n + 1} Test the convergence of the series. \sum_{n=1}^{\infty }\frac{(2...
b_n=ne^(-n)= n(e^n)>0 for n≥q 1. \( b_n\) is decreasing for n≥q 1 since (xe^(-x))'=x(-e^(-x))+e^(-x)=e^(-x)(1-x)<0>1.Also, \lim\limits_{n\to\infty}b_{n}=0 since \lim\limits_{x\to\infty}\dfrac {1}{e^{x}}=0. Thus, the series \sum\limi...
百度试题 结果1 题目Test the series for convergence or divergence.∑_(n=1)^∞(1⋅3⋅5⋅⋯⋅(2n-1))/(2⋅5⋅8⋯⋯(3n-1)) 相关知识点: 试题来源: 解析 C 反馈 收藏
Read what a p-series is and some examples of it. Learn the harmonic series and the p-series test for convergence to prove if it is convergent or...
Divergence Test The simplest test to be used to check the convergence or divergence of series (infinite sums) is the Divergence Test: if the sequence {eq}a_{n} {/eq} does not converge to {eq}0 {/eq}, then the series {eq}\sum a_n {/eq} diverges. Answer and ...
A test exists to describe the convergence ofallp-series. That test is called thep-series test,which states simply that: If p > 1, then the series converges, If p ≤ 1, then the series diverges. Here are some examples ofconvergent series: ...
Test the series for convergence or divergence.∑limits^∞_(n=2) 1((ln n)^(ln n)) 相关知识点: 试题来源: 解析 Note that (ln n)^(ln n)=(e^(ln ln n))^(ln n)=(e^(ln n))^(ln ln n)=n^(ln ln n) and ln ln n→ ∞ as n→ ∞ , so ln ln n>2 for sufficiently ...
Determine the convergence or divergence of the series using the Limit Comparison Test. ∑limits _(n=1)^n 1(√ (n(n+1))) ( ) A. Converges using ∑limits _(n=1)^∞ 1(n^2) B. Converges using ∑limits _(n=1)^∞ 1(n(n+1)) C. Diverges using ∑limits _(n=1)^∞ 1(√ ...
The Ratio Test The Integral Test The Comparison Test Absolute Convergence vs. Conditional Convergence Summary of Tests Taylor and Maclaurin Series Quizzes See All A Series of Seriously Simple Series Questions Burgers and Hotdogs: The All Star Examples of Mathematical Series The Series Finale Terms ...