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
Radius of Convergence: Suppose {eq}\sum\limits_{n = 1}^\infty {{a_n}} x^n {/eq} be a power series. Then a real number {eq}R {/eq} is said to be the radius of convergence of the power series if the series if convergent for al...
Radius of Convergence: The radius of convergence of the series {eq}\displaystyle \sum c_n (x-b)^n {/eq} is {eq}R {/eq} if values of {eq}x {/eq} for which this series converges can be found using the inequality {eq}|x-b|<R {/eq}. ...
Suppose that the radius of convergence of the power series ∑limits c_nx^n is R. What is the radius of convergence of the power series ∑limits c_nx^(2n)? 相关知识点: 试题来源: 解析 Since ∑limits c_nx^n converges whenever x R, ∑limits c_nx^(2n)=∑limits c_n(x^2)^n ...
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...
If the radius of convergence of the power series ∑limits ^m_(n=0)C_nx^n is 10, what is the radius of convergence of the series ∑_(n=1)^∞ n c_n x^(n-1)? Why? 相关知识点: 试题来源: 解析 If f(x)=∑limits _(n=0)^(∞ )c_nx^n has radius of convergence 10, ...
A、细胞内染色体数目比二倍体增加一条或数条 B、细胞内染色体数目比二倍体减少一条或数条 C、染色体数目在二倍体的基础上整组地增加 D、染色体数目在二倍体的基础上整组地减少 E、染色体数没有变化 点击查看答案 单项选择题 If converges and diverges, then the convergence radius of power series is 1. ...
What is the power series representation ofx21+x3? Power Series Representation; Radius of Convergence: The convergence of a power series[f(x)=∑n=0∞an]depends on the limit of the ratio of its consecutive terms(an,an+1). It may happen that the value of this limit remains less than ...
Informally, the assertion that is an approximate group containing as a “bounded index approximate subgroup” is equivalent to being covered by a bounded number of shifts of , where approximately normalises in the sense that and have large intersection. Thus, to classify all such , the problem ...
Finally, the irrationality of (Erdős problem #68) is completely open. On the other hand, it has long been known that if the sequence grows faster than for any , then the Ahmes series is necessarily irrational, basically because the fractional parts of can be arbitrarily small positive ...