Question

1+1/2+1/3+1/4+…+1/16的整数部分的值是_____.

Answer 1

A=1+1/2+1/3+1/4+1/5+.+1/15+1/16

=1+1/2+(1/3+1/4)+(1/5+1/6+1/7+1/8)+(1/9+...+1/15+1/16)

>1+1/2+(1/4+1/4)+(1/8+1/8+1/8+1/8)+(1/16+...+1/16+1/16)

=1+1/2+(1/4×2)+(1/8×4)+(1/16×8)

=1+1/2+1/2+1/2+1/2=3

另一方面,

A=1+1/2+1/3+1/4+1/5+.+1/15+1/16

=1+1/2+(1/3+1/4+1/5)+(1/6+1/7+1/8)+(1/9+1/10+1/11)+(1/12+1/13+1/14+1/15+1/16)