1／35+1／70+1／350+1／546+1／7903怎样简算?

题目

1／35+1／70+1／350+1／546+1／7903怎样简算?

答案

1/35+1/70+1/350+1/546+1/7903
=1/2*(1/5-1/7)+1/4*(1/5-1/7)+1/91*(1/2-1/3)+1/7*1/1129
后面不知道了
直接两项一通分求吧
原式=3/70+1/350+1/546+1/7903
=8/175+1/546+1/7903
=8/(5*37)+1/(2*3*91)+1/(7*1129)
分母之间全部互质 通分
=(8*6*91+5*37)/(2*3*5*37*91)+1/(7*1129)
=(7*11*59)/(2*3*5*37*91)+1/(7*1129)
=(7*11*59*7*1129+2*3*5*37*91)/(2*3*5*37*91*7*1129)
=(5143477*7)/(2*3*5*7*37*91*1129)=5143477/114040290
或者1/35+1/70+1/350+1/546+1/7903 = 0.047672321773296