Question

1/2 +5/6 + 11/12 ... + 89/90 + 109/110 + 10/11

Answer 1

1/2 + 5/6 +11/12 +...+ 89/90 + 109/110 + 10/11

= (1 - 1/2) + ( 1 - 1/6) + (1 - 1/12) + (1 - 1/20) +( 1 - 1/30) +... + (1 - 1/90) + (1- 1/110) + 10/11

= 1 x 10 –(1/2 + 1/6 + 1/12 + 1/20 +……..+ 1/90 + 1/110) + 10/11

= 10 – (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +……+ 1/9 - 1/10 + 1/10 - 1/11 ) + 10/11

= 10 – (1 - 1/11) + 10/11

= 10 - 10/11 + 10/11

= 10