a) = 1/5.6 + 1/6.7 + 1/7.8 + .. + 1/10.11
= 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11
= 1/5 - 1/11
= 6/55
b) 2/35 + 2/63 + 2/99 + .. + 2/255
= 2/5.7 + 2/7.9 + 2/9.11 + 2/11.13 + 2/13.15 + 2/15.17
= 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17
= 1/5 - 1/17
= 12/85