早教吧 育儿知识 作业答案 考试题库 百科 知识分享

n+2n^2+3n^3+...kn^k=?万分感激.

题目详情
n+2n^2+3n^3+...kn^k=?万分感激.
▼优质解答
答案和解析
当n=1时原式=1+2+3+……+k = k(k+1)/2当n≠1时设:S=n+2n^2+3n^3+...kn^k则:nS= n^2+2n^3+……+(k-1)n^k+kn^(k+1)则:(1-n)S=n+n^2+n^3+……+n^k - kn^(k+1)=n【1-n^k】/(1-n) - kn^(k+1)=【n-n^(k+1)】/(1-n) ...