幂级数求和,:∑(n从1到正无穷) n*(n+2)*x^n
来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/04/27 16:21:51
幂级数求和,:∑(n从1到正无穷) n*(n+2)*x^n
∑(n从1到正无穷) n(n+2)x^n
=x∑(n从1到正无穷) n(n+2)x^(n-1)
=x∑(n从1到正无穷)[(n+2)x^n]′
=x[∑(n从1到正无穷)(n+2)x^n]′
∑(n从1到正无穷)(n+2)x^n
=1/x[∑(n从1到正无穷)(n+2)x^(n+1)]
=1/x∑(n从1到正无穷)[x^(n+2)]′
=1/x[∑(n从1到正无穷)x^(n+2)]′
=1/x[x³/(1-x)]′
=x(3-2x)/(1-x)²
原式=x[x(3-2x)/(1-x)²]′
=x(3-x)/(1-x)³
=x∑(n从1到正无穷) n(n+2)x^(n-1)
=x∑(n从1到正无穷)[(n+2)x^n]′
=x[∑(n从1到正无穷)(n+2)x^n]′
∑(n从1到正无穷)(n+2)x^n
=1/x[∑(n从1到正无穷)(n+2)x^(n+1)]
=1/x∑(n从1到正无穷)[x^(n+2)]′
=1/x[∑(n从1到正无穷)x^(n+2)]′
=1/x[x³/(1-x)]′
=x(3-2x)/(1-x)²
原式=x[x(3-2x)/(1-x)²]′
=x(3-x)/(1-x)³
幂级数求和,:∑(n从1到正无穷) n*(n+2)*x^n
求幂级数(求和符号n从1到无穷)[(n^2+1)/n]*x^n的和函数
幂级数求和公式∑ ((-1)^n )*(x^(2n+1))/(2n+1)!n为0到无穷
幂级数求和:0到正无穷x^n/(n+1)怎么作,
求幂级数的和函数 S(x)= (x-1)^n/[n2^n] (n从1到无穷,求和)
n从1到无穷,n^2/n!级数求和
级数求和问题:求:∑1/(1+n^2)(n从1到正无穷)
求幂级数∑(n从1到无穷)(n+1)x^n的和函数
常数项级数求和 比如n从一到无穷,n除以2的n次方,化成幂级数nx^n 然后X带1/2,求和,幂级数还要讨论收敛
求幂级数∑{n=1到正无穷} [(x-1)^n]/n的收敛区间与和函数
求幂级数 n从0到无穷,n*x^(2n)的和函数?
几个级数求和问题 1.n(n+1)/2^n (n从1到正无穷) 2.2^n/3^n(2n-1) (n从1到正无穷)