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. ...
Bringing convergence to the metro Designed for multi-layer convergence, WaveRouter family of coherent metro routers can cost-effectively address unprecedented demands for coherent routing, or the convergence of IP and optical layers. The WaveRouter family is designed for this convergence in the metro ...
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{(-1)^n(x-y)^n}{5^n(n+2)} {/eq}?Question:What is the radius of convergence of the series {eq}\sum_{n=1}^\infty \frac{(-1)^n(x-y)^n}{5^n(n+2)} {/eq}?R...