Test the series for convergence or divergence. ∑limits ^∞_(n=1)(-1)^(n+1)ne^(-n) 相关知识点: 试题来源: 解析 converges 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....
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
Test the series for convergence or divergence. ∑n=1∞1n+3n Ratio Test: The ratio test is a series convergence test that allows us to determine the convergence of a series if its terms consist of different types of expressions, such as factorials, exponents, and rati...
Test the series for convergence or divergence. ∑m=1∞cos(m). Condition of convergence For a numerical series to be convergent, it is necessary that the limit of the general term be equal to zero. That is, if the limit is not equal to zero, we will say that th...
Test the series for convergence or divergence. ∑k = 1∞12+sink 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 an does not converge to 0, then the series ∑an ...
Test the series for convergence or divergence. 1. \sum_{1}^{\infty }\mid _{\left ( (1/n^{3})+(1/3^{n}) \right )}\2. \sum_{1}^{\infty }\mid _1/(n\ast \sqrt{ (\ln n })\3. \sum_{1}^{\infty }\mid _(3^{n ...
Homework Statement Test the series for convergence or divergence Homework Equations A_n = Ʃ 1/(2+sin(k)) from k = 1 to ∞ The Attempt at a Solution I looked at this and I thought that sin(k) does not have a limit as k goes to infinity. So I was thinking that Lim k--> ∞...
Now, we're going to test the convergence or divergence of some series by doing some reasoning similar to what we did when studying left-hand and right-hand sums for integrals. Integral Test: Let f be a non-negative decreasing function on [c,∞) where c is an integer. If the integral...
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Kummer testing the convergence or divergence of positive series. Comments on the power of Kummer's test.doi:10.2307/2974907Jingcheng TongAmerican Mathematical MonthlyJ. Tong, Kummer'sTest Gives Characterizations for Convergence or Divergence of all Positive Series, The American Mathematical Monthly, Vol...