Question

2/15 + 2/35 + 2/63 + 2/99 + .... + 2/575 + 2/675

Answer 1

= 2/3×5 + 2/ 5×7 + 2/ 7×9 + 2/ 9×11 + ...... + 2/ 23×25+ 2 / 25×27

=1/3 - 1/5 + 1/5 -1/7 + 1/7 -1/9 +1/9 -1/11+.......+1/23- 1/25 + 1/25 -1/27

= 1/3 - ( 1/5+1/5 -1/7 +1/7 - 1/9 +1/9-1/11 +........+ 1/23 -1/25 + 1/25 )-1/27

=1/3 - 1/27= 9/27 - 1/27= 8/27