1／3＋1／8＋1／15＋．．．．．．1／120=?

1/3=(1/2)*(1-1/3)
1/8=(1/2)*(1/2-1/4)
1/15=(1/2)*(1/3-1/5)
.
1/120=(1/2)*(1/10-1/12)
所以
原式=(1/2)*(1-1/3+1/2-1/4+1/3-1/5+...+1/9-1/11+1/10-1/12)
=(1/2)*(1+1/2-1/11-1/12)
=(1/2)*(175/132)
=175/264