1/1×2+1/3×4+1/5×6+1/7×8+……+1/1011×1012请问这题怎么解?1/1×2+1/3×4+1/5×6+1/7×8+……+1/1011×1012是这样的.

Question

1/1×2+1/3×4+1/5×6+1/7×8+……+1/1011×1012 请问这题怎么解?
1/1×2+1/3×4+1/5×6+1/7×8+……+1/1011×1012是这样的.

Answer 1

裂项求和,1/(n*(n+1))=1/n-1/(n+1)
所以原式=1/1-1/2+1/2-1/3+.+1/1011-1/1012=1-1/1012=1011/1012