1+2+3+.+n=n(n+1)/2
1/(1+2+3+.+n)=2/n(n+1)
1/(1+2) + 1/(1+2+3) + 1/1+2+3+4 + …… 1/1+2+……+199+200
=2/2*3+2/3*4+2/4*5+.+2/200*201
=2(1/2*3+1/3*4+1/4*5+.+1/200*201)
=2(1/2-1/3+1/3-1/4+1/4-1/5+.+1/200-1/201)
=2*(1/2-1/201)
=2*1/2-2*1/201
=1-2/201
=199/201