[1/(5×9)]+[1/(9×13)]+[1/(13×17)]+…+[1/(101×105)]=?
热心网友
原式=1/4*[4/(5*9)+4/(9*13)+4/*13*17)+......+4/(101*105)]=1/4*[(9-5)/(5*8)+.........+(105-101)/(101*105)]=1/4*[(1/5-1/9)+(1/9-1/13)+(1/13-1/17)+......+(1/101-1/105)]=1/4*(1/5-1/105)=1/4*(21-1)/105=1/4*20/105=1/21