1/3+1/6+1/10+1/15+1/(1+2+3+4+5+...n)=?找规律_数学解答

1/3+1/6+1/10+1/15+1/(1+2+3+4+5+...n)=?找规律

人气：184 ℃　时间：2020-07-06 01:30:00

解答

原式=1/((1+2)*2/2)+1/((1+3)*3/2)+1/((1+4)*4/2)+……+1/((1+n)*n/2)
=2/(2*3)+2/(3*4)+2/(4*5)+2/(5*6)+……+2/(n*(n+1))
=2(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/n-1/(n+1))
=(n-1)/(n+1)