Question

1/3+1/15加35分之一加63分之一，简便运算？

Answer 1

1/3+1/15加35分之一加63分之一，简便运算如下：
1/3+1/15+1/35+1/63
=5/15+1/15+1/35+1/63
=6/15+1/35+1/63
=2*3/5*3+1/(5*7)+1/(7*9)
=2/5+1/(5*7)+1/(7*9)
=(2*7)/(5*7)+1/(5*7)+1/(7*9)
=(14+1)/(5*7)+1/(7*9)
=(5*3)/(5*7)+1/(7*9)
=3/7+1/(7*9)
=(3*9)/(7*9)+1/(7*9)
=28/(7*9)
=7*4/(7*9)
=4/9

Answer 2

把式子看成1/3+1/（3×5）+1/（5×7）+1/（7×9）
举个例子1/（3×5）=1/2×（1/3-1/5）
把式子中的相同数看没变成1/2-1/2×1/9=4/9
ok

Answer 3

1/3+1/15+1/35+1/63
=1/（1×3）+1/（3×5）+1/（5×7）+1/（7×9）
=（1－1/3）×1/2+（1/3－1/5）×1/2+（1/5－1/7）×1/2+（1/7－1/9）×1/2
=1/2×（1－1/3+1/3－1/5+1/5－1/7+1/7－1/9）
=1/2×8/9
=4/9