a) 1/1.2 + 1/2.3 +......+ 1/99.100
=1-1/2+1/2-1/3+1/3-1/4+.....+1/99-1/100
=1-1/100
=99/100.
b) 1/4.5+ 1/5.6+ ......+1/78.79 + 1/79.80
= 1/4-1/5+1/5-1/6+1/6-1/7+...+1/79-1/80
= 1/4-1/80
= 19/80
c) 2/3.5 + 2/5.7 +.......+ 2/37.39
= 2/3-2/5+2/5-2/7+2/7-2/9+...+2/37-2/39
= 2/3 - 2/39
= 26/39
d) 3/4.7 + 3/7.10 + ......+ 3/73.76
= 3/4-3/7+3/7-3/9+...+3/73-3/76
= 3/4-3/76
= 54/76 = 27/38