计算1/1*6+1/6*11+1/11*16+1/16*21+.+1/51*56
问题描述：
计算1/1*6+1/6*11+1/11*16+1/16*21+.+1/51*56
答
因为
1/1* 6 = (1/5)(1 - 1/6)
1/6*11 = (1/5)(1/6 - 1/11)
依此类推
1/51*56 = (1/5)(1/51 - 1/56)
所以
1/1*6+1/6*11+1/11*16+1/16*21+.......+1/51*56
= (1/5)(1 - 1/6 + 1/6 - 1/11 + ... + 1/51 - 1/56)
= (1/5)(1 - 1/56)
= 11/56
答
1/1*6+1/6*11+1/11*16+1/16*21+.......+1/51*56
=(1-1/6)*1/5+(1/6-1/11)*1/2+……+（1/51-1/56）*1/5
=（1-1/6+1/6-1/11+……+1/51-1/56）*1/2
=（1-1/56）*1/5
=11/56
答
1/(1*6)=1/5*(/1-1/6)
1/(6*11)=1/5*(1/6-1/11)
……
1/1*6+1/6*11+1/11*16+1/16*21+.+1/51*56
=1/5*（1/1-1/6+1/6-1/11+1/11-1/16+……+1/51-1/56）
=1/5*(1-1/56)
=11/56