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Answers to four questions in the 39th issue of the fifth grade mathematics in the Report on the Development of Teenagers' Intelligence.
1/( 1+2)+ 1/(2+3)+ 1/(3+4)+............+ 1/(99+ 100)

=( 1- 1/2)+( 1/2- 1/3)+( 1/3- 1/4)+.........+( 1/99- 1/ 100)

= 1- 1/2+ 1/2- 1/3+ 1/3- 1/4+...............+ 1/99- 1/ 100

= 1- 1/ 100

=99/ 100

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