第100个数是1/100*101=1/10100,这100个数的和是100/101.
1/2+1/6+1/20+……+1/10100
=1/1*2+1/2*3+1/3*4+……+1/100*100
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/100-1/101
=1-1/101
=100/101