Question

1/2+1/6+1/12+1/20+1/30+ ...+1/420 =

Answer 1

1/2+1/6+1/12+1/20+1/30+ ...+1/420 =

=1/(1·2)+1/(2·3)+1/(3·4)+1/(4·5)+1/(5·6)+.....+1/(20·21)

=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+....+(1/20-1/21)

=1/1-1/21

=20/21

Poti utiliza formula:1/(1·2)+1/(2·3)+1/(3·4)+1/(4·5)+.....+1/[n·(n+1)]=n/(n+1)