`1/3 +1/2.4 +1/3.5 + 1/4.6 +....+1/198.200 +1/199.201 + 1/2.201`

`=(1/1.3+1/3.5+1/5.7+....+1/199.201)+(1/2.4+1/4.6+1/6.8+....+1/198.200)+1/2.201`

`=1/2(2/1.3+2/3.5+2/5.7+...+2/199.201)+1/2(2/2.4+2/4.6+2/6.8+...+2/198.200)+1/402`

`=1/2(1/1-1/3+1/3-1/5+1/5-1/7+...+1/199-1/201) + 1/2 ( 1/2-1/4+1/4-1/6+1/6-1/8+...+1/198-1/200) +1/402`

`=1/2 (1-1/201) + 1/2(1/2-1/200)+1/2*1/201`

`=1/2(1-1/201+1/2-1/200+1/201)`

`=1/2(1+1/2-1/200)`

`=1/2(200/200+100/200-1/200)`

`=1/2*299/200`

`=299/400`