Question

一道奥数计算题

要详细的过程

Answer 1

令a=1-1/2-1/3-...-1/6;b=1/2+1/3+...+1/6
则原式=(a+1/6)×b-a×(b-1/6)
=ab+b/6-ab+a/6
=(a+b)/6
=1/6

Answer 2

（1-1/2-```-1/5)(1/2+1/3+```+1/6)=（1-1/2-```-1/5)(1/2+1/3+```+1/5)+（1-1/2-```-1/5)/6
（1-1/2-```-1/6)(1/2+1/3+```+1/5)=（1-1/2-```-1/5)(1/2+1/3+```+1/5)-（1/2+1/3+```+1/5)/6
所以（1-1/2-```-1/5)(1/2+1/3+```+1/6)-（1-1/2-```-1/6)(1/2+1/3+```+1/5)=（1-1/2-```-1/5+1/2+1/3+```+1/5)/6=1/6

Answer 3

原式=（1*1/2+...+1*1/6-1/2*1/2-1/2*1/3-.........1/5*1/6）-（1*1/2...+1*1/5-1*1/2-......1/6*1/5）=1/6