\(=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+.......+\frac{1}{31.37}=\frac{1-\frac{1}{37}}{6}\)
=1/1×7+1/7×13+1/13×19+...+1/31×37
=1/6×(1-1/7)+1/6×(1/7-1/13)+1/6×(1/13-1/19)+...+1/6×(1/31-1/37)
=1/6×(1-1/7+1/7-1/13+1/13-1/19+...+1/31-1/37)
=1/6×(1-1/37)
=1/6×36/37
=6/37