1/1×2+1/2×3+1/3×4+...+1/19×20等于多少1/1×4+1/4×7+1/7×10+...+1/91×94等于多少

1/1×2+1/2×3+1/3×4+...+1/19×20等于多少1/1×4+1/4×7+1/7×10+...+1/91×94等于多少
1/1×2+1/2×3+1/3×4+...+1/19×20等于多少
1/1×4+1/4×7+1/7×10+...+1/91×94等于多少

1/1×2+1/2×3+1/3×4+...+1/19×20等于多少1/1×4+1/4×7+1/7×10+...+1/91×94等于多少
1/1*2+1/2*3+1/3*4+...+1/19*20
=(1-1/2+1/2-1/3+1/3-1/4+...+1/19-1/20)
=(1-1/20)
=19/20
1/n*(n+3)=1/3[1/n-1/(n+3)]
所以 1/1*4+1/4*7+1/7*10+...+1/91*94
=1/3[(1-1/4)+(1/4-1/7)+...+(1/91-1/94)]
=1/3(1-1/94)
=31/94