5/（3×7）＋5/（7×11）+5/（11×15）+……+5/（55×59）
=5*1/4[1/3-1/7]+5*1/4[1/7-1/11]+.+5*1/4[1/55-1/59]
=5/4*[1/3-1/7+1/7-1/11+...+1/55-1/59]
=5/4*[1/3-1/59]
=70/177