1/30+1/42+1/56+1/72+1/90+1/110=?

题目

1/30+1/42+1/56+1/72+1/90+1/110=?

答案

1/2*15+1/2*21+1/2*28+1/2*36+1/2*45+1/2*55
=1/2*(1/15+1/21+1/28+1/36+1/45+1/55)
=1/2*(1/3*5+1/3*7+1/4*7+1/4*9+1/5*11)
=1/2*[1/3(1/5+1/7)+1/4(1/7+1/9)+1/55]
=1/2*[1/3(12/35)+1/4(16/63)+1/55]
=1/2*(4/35+4/63+1/55)
=1/2*[(4*63)/35*63+(4*35)/35*63+1/55]
=1/2*(252/2205+140/2205+1/55)
=1/2*(392/2205+1/55)
=1/2*[(392*11)/2205*11+441/55*441]
=1/2*(4312/24255+441/24255)
=1/2*(4753/24255)
=4753/48510
这是笨办法,有好办法的朋友发一下