a. 1 1 1 1 --------+ ------- + ------- + .................... --------------- 1x2 2x3 3x4 99x100 b. 2 2 2 2 --------- + -------- + ---------- + ................. ---------------- 2x4 4x6 6x8 98x100

`1/(1xx2)+1/(2xx3)+1/(3xx4)+.....1/(99xx100)`

`=1/1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100`

`=1/1-1/100`

`=100/100-1/100`

`=99/100`

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`2/(2xx4)+2/(4xx6)+2/(6xx8)+.........2/(98xx100)`

`=1/2 xx ( 2/2-2/4)+ 1/2 xx ( 2/4-2/6)+1/2xx(2/6-2/8)+.......1/2xx(2/98-2/100)`

`=1/2xx(2/2-2/4+2/4-2/6+2/6-2/8+.........+2/98-2/100)`

`=1/2xx(2/2-2/100)`

`=1/2xx(100/100-2/100)`

`=1/2 xx 98/100`

`=98/200`

`=49/100`