化简计算:3*1/7+7*1/11+11*1/15+15*1/19+19*1/23+23*1/27+27*1/31+31*1/35+35*1/39+39*1/43+43*1/47+47*1/51+51*1/55+55*1/59=?

Question

化简计算:3*1/7+7*1/11+11*1/15+15*1/19+19*1/23+23*1/27+27*1/31+31*1/35+35*1/39+39*1/43+43*1/47+47*1/51+51*1/55+55*1/59=?

Answer 1

裂项法：1/3*7+1/7*11+1/11*15+1/15*19+1/19*23+1/23*27+1/27*31+1/31*35+1/35*39+1/39*43+1/43*47+1/47*51+1/51*55+1/55*59
=1/4*（1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+……+1/47-1/51+1/51-1/55+1/55-1/59）
=1/4*（1/3-1/59）
=1/4*56/171
=14/171