Question

1 supra 2+1 supra 6+1supra 12+1 supra 20+....+1 supra 2017*2018

Answer 1

1/2+1/6+1/12+1/20+....+1/(2017x2018)=
=1/(1x2) +1/(2x3) +1/(3x4) +...1/(2016x2017)+1/(2017x2018)=
=(1-1/2) +(1/2 -1/3) +(1/3-1/4)+...+(1/2016 -1/2017)+(1/2017 -1/2018)=
=1-1/2 +1/2 -1/3 +1/3-1/4+...+1/2016 -1/2017+1/2017 -1/2018=
=(se observa ca inafara de primul si ultimul termen, restul se reduc)=
=1- 1/2018=2017/2018