Question

求a=(1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9)*15/22的整数部分

Answer 1

因为：1/a+1/b=(a+b)/(a*b)

所以：a=101/84,其整数部份就是1

=[(1/2+1/9)+(1/5+1/6)+(1/3+1/8)+(1/4+1/7)]*15/22

=11[(1/18+1/30)+(1/24+1/28)]*15/22

=11*48[1/(18*30)+1/(24*28)]*15/22

=24*15*[1/(18*30)]+24*15*[1/(24*28)]

=2/3+15/28

=101/84