通项公式,第n个加式可以表述成：
1/(1 + 2 + 3 + ...+ n)
= 1/[n(n + 1)/2]
= 2/[n(n + 1)]
= 2[1/n - 1/(n + 1)]
那么代入：
1/1 + 1/(1 + 2) + 1/(1 + 2 + 3) + .+ 1/(1 + 2 + 3 + ...+ 50)
= 1 + 2/(2*3) + 2/(3*4) + .+ 2/(50*51)
= 1 + 2*(1/2 - 1/3) + 2*(1/3 - 1/4) + ...+ 2*(1/50 - 1/51)
=1 + 2*(1/2 - 1/51)
=100/51