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Interesting math problems in the second volume of the seventh grade
1 calculation

( 1+ 1/ 1 1+ 1/ 13+ 1/ 17)( 1/ 1 1+ 1/ 13+ 1/ / kloc-0/7+ 1/ 19)-( 1+ 1/ 1 1+ 1/ 13+ 1/ 17+ 1/ 19)( 1/ / kloc-0/ 1+ 1/ 13+ 1/ 17)

2 calculation

( 1/2+ 1/3+....+ 1/2005)( 1+ 1/2+ 1/3+....+ 1/2004)-( 1+ 1/2+...+ 1/2005)( 1/2+ 1/3+...+ 1/2004)

The first question:

Take the minus sign behind this formula apart first:

( 1+ 1/ 1 1+ 1/ 13+ 1/ 17)( 1/ 1 1+ 1/ 13+ 1/ / kloc-0/7+ 1/ 19)-( 1+ 1/ 1 1+ 1/ 13+ 1/ 17+ 1/ 19)( 1/ / kloc-0/ 1+ 1/ 13+ 1/ 17)

=( 1+ 1/ 1 1+ 1/ 13+ 1/ 17)( 1/ 1 1+ 1/ 13+ 1/ / kloc-0/7+ 1/ 19)-( 1 + 1/ 1 1+ 1/ 13+ 1/ 17)( 1/ 1 1+ / kloc-0// 13+ 1/ 17)- 1/ 19( 1/ 1 1+ 1/ 13+ 1/ 17)

=( 1+ 1/ 1 1+ 1/ 13+ 1/ 17)( 1/ 1 1+ 1/ 13+ 1/ / kloc-0/7+ 1/ 19- 1/6 5438+0 1- 1/ 13- 1/ 17)- 1/ 19( 1/ 1 1+ 1/ 13+ 1/ 17)

= 1/ 19( 1+ 1/ 1 1+ 1/ 13+ 1/ 17)- 1/ 19( 1/ 1 1+ 1/ 13+ 1/ 17)

= 1/ 19( 1+ 1/ 1 1+ 1/ 13+ 1/ 17- 1/ 1 1- 1/ 13- 1/ 17)

= 1/ 19

The second question:

Like the solution to the previous question, first disassemble the formula behind the minus sign:

( 1/2+ 1/3+....+ 1/2005)( 1+ 1/2+ 1/3+....+ 1/2004)-( 1+ 1/2+...+ 1/2005)( 1/2+ 1/3+...+ 1/2004)

=( 1/2+ 1/3+....+ 1/2005)( 1+ 1/2+ 1/3+....+ 1/2004)-( 1/2+ 1/3+...+ 1/2005)( / kloc-0//2+ 1/3+...+ 1/2004)-( 1/2+ 1/3+...+ 1/2004)

=( 1/2+ 1/3+....+ 1/2005)( 1+ 1/2+ 1/3+....+ 1/2004 - 1/2- 1/3-...- 1/2004)-( 1/2+ 1/3+...+ 1/2004)

=( 1/2+ 1/3+....+ 1/2004+ 1/2005)-( 1/2+ 1/3+...+ 1/2004)

= 1/2005

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