幂级数求和,:∑(n从1到正无穷) n*(n+2)*x^n_数学解答

幂级数求和,:∑(n从1到正无穷) n*(n+2)*x^n

人气：295 ℃　时间：2019-11-18 10:00:57

解答

∑(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^(...