a=1/(1·2)+1/(2·3)+1/(3·4)+.....+1/[n·(n+1)]; n∈n*
a=1/1 - 1/2 + 1/2 - 1/3 + 1/3 -1/4 +.....+1/n -1/(n+1)
a=1 - 1/(n+1)
a=n/(n+1)
a=0,999=999/1000
n/(n+1)=999/1000 => n=999
