5/6 +11/12 +...+2549/2550=[1- 1/(2×3)]+[1- 1/(3×4)]+...+[1- 1/(50×51)]=1×(50-1) -[1/(2×3) +1/(3×4)+...+1/(50×51)]=49- (1/2 -1/3 +1/3 -1/4+...+1/50 -1/51)=49- (1/2 - 1/51)=4949/102
如图
