微积分的知识问题:Radius and interval of convergence 半径与间隔聚集 题目是“1.find radius and interval of convergence of series .2.find radius and interval of convergence of series .“由于题不好打,我写在纸上了:就是那些我写why的地方我实在是不知道如
Convergence of Power Series by Ratio Test: Every power series has a radius of convergence. It can be found in the following way- If {eq}\sum\limits_{n=0}^{\infty}a_nx^n {/eq} is a power series of real number such that {eq}\lim\limits_{n \to \infty}\left| \frac...
题目Find the radius of convergence of the power series, where c>0 and k is a positive integer.$$ \sum _ { n = 1 } ^ { \infty } \fra c { ( x - c ) ^ { n - 1 } } { c ^ { n - 1 } } $$ 相关知识点: 试题来源: 解析 R=c ...
Find the interval,I, of convergence of the series. Radius and Interval of Convergence of a Series: We use the Ratio test to find the radius and interval of convergence of a series. Ratio test is given byL=limn→∞|bn+1bn| b
convergence from it. The easiest way to get the interval of convergence is to use the Ratio test for series. Answer and Explanation:1 {eq}\; \sum_{n=0}^{\infty} \; (-1)^{n - 1} \left ( \frac{n}{n^2 + 1} \right ) \left ( \frac{(...
结果1 题目 Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)∑limits_(n=0)^∞(x^(3n+1))((3n+1)!) 相关知识点: 试题来源: 解析 (-∞,∞) 反馈 收藏 ...
Answer to: Find the series interval of convergence and within this interval, the sum of the series. sum_n=0^infty (x-3)^2n/36^n By signing up,...
【题目】Find the radius of convergence and interval of convergence$$ \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { n ^ { 2 } x ^ { n } } { 2 ^ { n } } $$ 相关知识点: 试题来源: 解析 【解析】 If$$ I f a _ { n } = ( - 1 ) ^ { n } \...
Find the radius of convergence and interval of convergence of the series {eq}\sum_{n=1}^\infty \frac{3^nx^n}{n^2} {/eq} Convergence of Power Series Consider the power series about the point {eq}x_0 {/eq}, that is, {eq}f(x) = \displayst...
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