Question

【要过程】(1+1/2+1/3+.+1/100)*(1/2+1/3+...+1/101)-(1/2+1/3+..+1/1

Answer 1

题目应该是求(1+1/2+1/3+……+1/100)*(1/2+1/3+……+1/101)-(1+1/2+1/3+……+1/101)*(1/2+1/3+……+1/100）的值

设1+1/2+1/3+……+1/100=A,1/2+1/3+……+1/101=B

所以B-A=1/101-1

因为1+1/2+1/3+……+1/101=1/2+1/3+……+1/101+1=B+1

1/2+1/3+……+1/100=1+1/2+1/3+……+1/100-1=A-1

所以原式=AB-（A-1)(B+1）

=AB-AB-A+B+1

=B-A+1

=1/101+1

=1/101