Intervals and stakes ?

Each ball has a diameter of $1~m$ and the distance between each sphere is $1~ m$ . This means, except the last ball every sphere has a separation of $1~m$ to its right. So,

$\text{Distance between the first and the last points} = 2 \times (Number~of~balls - 1) + diameter~of~the~last~ball$

$\implies 2 \times (1000 - 1) + 1$

$\implies 2 \times 999 + 1$

$\implies 1998 + 1 = 1999$

Hint : if there were only 2 balls, how many intervals would be ? If there were 10 balls, how many intervals ? Once known the number of intervals, do not forget to count, between each extreme ball, all the diameters and all the intervals. They are on a straight line, without triangular arrangement, without matter nor mass, without relativity nor universe around.