1/2×2!+2/3×3!+3/4×4!+...+8/9×9!【递等式】
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 01:27:31
![1/2×2!+2/3×3!+3/4×4!+...+8/9×9!【递等式】](/uploads/image/z/9457597-37-7.jpg?t=1%2F2%C3%972%21%2B2%2F3%C3%973%21%2B3%2F4%C3%974%21%2B...%2B8%2F9%C3%979%21%E3%80%90%E9%80%92%E7%AD%89%E5%BC%8F%E3%80%91)
1/2×2!+2/3×3!+3/4×4!+...+8/9×9!【递等式】
1/2×2!+2/3×3!+3/4×4!+...+8/9×9!【递等式】
1/2×2!+2/3×3!+3/4×4!+...+8/9×9!【递等式】
n/(n+1)*(n+1)!
=n*n!
=[(n+1-1)*n!
=(n+1)*n!-n!
=(n+1)!-n!
所以原式=2!1-1!+……+9!-8!
=9!-1!
=362879