1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42
=(1 - 1/2) + (1- 1/6) + (1 - 1/12) + ( 1- 1/20) +(1 - 1/30) + (1 - 1/42)
=6 – (1/2+ 1/6+ 1/12+ 1/20+ 1/30+ 1/42)
=6 – [ 1/(1x2) + 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) + 1/(6x7)]
=6 – ( 1- 1/2 + 1/2 -1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 )
=6 - ( 1 - 1/7)
= 6- 6/7
=36/ 7