计算:1/1x2+1/2x3+1/3x4+.+1/(n-1)n
问题描述:
计算:1/1x2+1/2x3+1/3x4+.+1/(n-1)n
答
1/1x2+1/2x3+1/3x4+.+1/(n-1)n观察一下1/1x2=1-1/21/2x3=1/2 -1/31/3x4=1/3 -1/4..1/(n-1)n=1/(n-1) - 1/n然后所有式子相加1/1x2+1/2x3+1/3x4+.+1/(n-1)n=1-1/2 +1/2-1/3+1/3-1/4+.-1/(n-1)+1/(n-1)-1/n=1-1/n=(n-1)...