5*9分之4+9*13分之4+13*17分之4+.101*105分之4=?简便方法!送分!
问题描述：
5*9分之4+9*13分之4+13*17分之4+.101*105分之4=?简便方法!送分!
答
1/(5*9)+1/(9*13)+...+1/(101*105)=(1/4)*(1/5-1/9)+(1/4)*(1/9-1/13)+...+(1/4)*(1/101-1/105)=(1/4)*(1/5)-(1/4)*(1/9)+(1/4)*(1/9)-(1/9)*(1/13)+...+(1/4)*(1/101)-(1/4)*(1/105)=(1/4)*(1/5)-(1/4)*(1/105)=(1/...