2/(1×6)+2/(6×11)+2/(11×16)+……+2/(101×106)的值是多少?

题目

2/(1×6)+2/(6×11)+2/(11×16)+……+2/(101×106)的值是多少?

答案

原式=2*(1/5)*(1-1/6+1/6-1/11+1/11-1/16+.+1/101-1/106)
=2*(1/5)*(1-1/106)
=21/53