Use the Ratio Test to find the radius of convergence.The ratio is ((x-7)^(n+1))(3^(n+1)(n+3)^4)⋅ (3^n(n+2)^4)((x-7)^n) = ( (n+2)(n+3))^4⋅ (x-7)3 . Find the limit: lim limits_(x→∞) ( (n+2)(n+3))^4⋅ (x-7)3 = (x-7)3 . So for...
试题来源: 解析 If k is any real number and |x|1, then (1+x)^2-∑_(n=0)^n(k/n)x^n =1+kx+(k(k-1))/(2!)x^2+(k(k-1)(k-2))/(3!)x^3+ The radius of convergence for the binomial series is 1. 反馈 收藏
Find the Taylor series for {eq}f(x)=\frac{1}{1 - x} {/eq} centered atc = 2. What is the radius of convergence? Convergence Radius and Series: If the development center is equal to zero, then we'll use the general expansion (from the table of Taylo...
What is the radius of convergence, {eq}\displaystyle R {/eq} for the function {eq}\displaystyle f(x) = \frac{1}{(7+x)^3} {/eq}.The radius of a Function:We can find a radius of a given function either by using the formula of the radius of convergence of a po...
Question: Consider the seriesf(x)=∑n=1∞64nx3nn(i) What is the radius of convergence of this series?Write the letter i if the radius is infinite.(ii) Find the series expansion, centered at x=0, for the derivative ...
Since ∑limits c_nx^n converges whenever x R, ∑limits c_nx^(2n)=∑limits c_n(x^2)^n converges whenever x^2 R ⇔ x <√ R, so thesecond series has radius of convergence √ R.结果一 题目 Supposethattheradiusofconvergenceofthepowerseries is . Whatistheradiusofconvergenceofthepowerser...
What is the radius o f convergence o f the power series cnx2n? 相关知识点: 试题来源: 解析 【解析】 Since cn" converges whenever |x|R , ∑c_nx^(2n)=∑_n^rC_n(x^2)^n converges whenever |x^2|R⇔|x|√(H^2) , so thesecond series has radius of convergence VR. ...
曲线下面积的积分 114-What is Integration Finding the Area Under a Curve 08:18 积分基本定理:重新定义积分 115-The Fundamental Theorem of Calculus Redefining Integration 09:38 积分的性质和定积分的计算 116-Properties of Integrals and Evaluating Definite Integrals 09:48 计算不定积分 117-Evaluating...
because the cost for atwisted paircable used with Ethernet is lower than that of a fiber optic cable, not counting costs for FC switches and connecting devices. It's also easier for twisted-pair cable to go around corners, whereas fiber optic cable must observe specific radius limits when tr...
What is the radius of convergence of the series {eq}\sum_{n=1}^{\infty} \frac{(2 x-3)^{2 n}}{4^n} {/eq}? (i) 1 (ii) 2 (iii) 3 (iv) 4 The Radius of Convergence of a Power Series: Suppose we have a power series given as...