来自阮建山的问题
一道数列求和题1/2n+3/4n+5/8n+...+(2n-1)/n*2^n
一道数列求和题
1/2n+3/4n+5/8n+...+(2n-1)/n*2^n
1回答
2020-11-15 21:02
一道数列求和题1/2n+3/4n+5/8n+...+(2n-1)/n*2^n
一道数列求和题
1/2n+3/4n+5/8n+...+(2n-1)/n*2^n
这道题用错位相减法.原式/2=1/4n+3/8n+...+(2n-1)/n*2^(n+1)所以原式/2=1/2n+2/4n+2/8n+...+2/n*2^n-(2n-1)/n*2^(n+1)n*原式/2=1/2+1-(1/2)^(n-1)-(2n-1)/2^(n+1)原式=3/n-(2n+7)/2^(n+1)