Question

1乘3乘5分之1+3乘5乘7分之1+5乘7乘9分之1+7乘9乘11分之1+9乘11乘13分之1+11乘13乘15分之1=

Answer 1

1/1×3×5=1/4×(1/1×3 -1/3×5)

1/3×5×7=1/4×(1/3×5 -1/5×7)

1/5×7×9=1/4×(1/5×7 - 1/7×9)

1/7×9×11=1/4×(1/7×9 -1/9×11)

.

1/11×13×15=1/4×(1/11×13 -1/13×15)

所有的等式相加有

1/1×3×5+1/3×5×7+1/5×7×9+.+1/11×13×15

=1/4×(1/1×3 -1/3×5 +1/3×5 -1/5×7+.+1/11×13 -1/13×15)

=1/4×(1/1×3 - 1/13×15)

=(1/4)×192/195

=16/195