ly137
幼苗
共回答了13个问题采纳率:92.3% 举报
1/2-1/3=1/(2×3)=1/6; 1/3-1/4=1/(3×4)=1/12
当n为不等于0的自然数时, 1/n-1/(n+1)=1/[n×(n+1)]
根据上述规律,所以有:
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(2010×2011)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2009-1/2010)+(1/2010-1/2011)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/1010+1/2010-1/2011
=1-1/2011
=2010/2011
1年前
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