`a)` `M=`$\dfrac{2}{3.5}$`+`$\dfrac{2}{5.7}$`+`$\dfrac{2}{7.9}$`+...+`$\dfrac{2}{97.99}$

`=`$\dfrac{1}{3}$`-`$\dfrac{1}{5}$`+`$\dfrac{1}{5}$`-`$\dfrac{1}{7}$`+...+`$\dfrac{1}{97}$`-`$\dfrac{1}{99}$

`=`$\dfrac{1}{3}$`-`$\dfrac{1}{99}$

`=`$\dfrac{33}{99}$`-`$\dfrac{1}{99}$

`=`$\dfrac{32}{99}$

`b)` `N=`$\dfrac{3}{5.7}$`+`$\dfrac{3}{7.9}$`+`$\dfrac{3}{9.11}$`+...+`$\dfrac{3}{197.199}$

`=`$\dfrac{3}{2}$$\left(\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+...+\dfrac{2}{197.199}\right)$

`=`$\dfrac{3}{2}$$\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{197}-\dfrac{1}{199}\right)$

`=`$\dfrac{3}{2}$$\left(\dfrac{1}{5}-\dfrac{1}{199}\right)$

`=`$\dfrac{3}{2}$$\left(\dfrac{199}{995}-\dfrac{5}{995}\right)$

`=`$\dfrac{3}{2}$ `.` $\dfrac{194}{995}$

`=`$\dfrac{194}{995}$

`a)`

`M = 2/(3 . 5) + 2/(5 . 7) + 2/(7 . 9) + ... + 2/(97 . 99)`

`M = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 2/97 - 2/99`

`M = 1/3 - 2/99`

`M = 32/99`

`b)`

`N = 3/(5 . 7) + 3/(7 . 9) + 3/(9 . 11) + ... + 3/(197 . 199)`

`N = (3/(5 . 7) + 3/(7 . 9) + 3/(9 . 11) + ... + 3/(197 . 199)) . 3/2`

`N = (1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + ... + 1/197 - 1/199) . 3/2`

`N = (1/5 - 1/199) . 3/2`

`N = 194/995 . 3/2`

`N = 291/995`