5) A = 1/(11.16) + 1/(16.21) + ... + 1/(96.101)
=> 5A = 5/(11.16) + 5/(16.21) + ... + 5/(96.101)
= 1/11 - 1/16 + 1/16 - 1/21 + ... + 1/96 - 1/101
= 1/11 - 1/101 = 90/1111
=> A = 18/1111
6) A = 1/(52.54) + 1/(54.56) + ... + 1/(98.100)
=> 2A = 2/(52.54) + 2/(54.56) + ... +2/(98.100)
= 1/52 - 1/54 + 1/54 - 1/56 + ... + 1/98 - 1/100
= 1/52 - 1/100 = 3/325
=> A = 3/650
7) A = 1/(1.4) + 1/(4.7) + ... + 1/(97.100)
=> 3A = 3/(1.4) + 3/(4.7) + ... + 3/(97.100)
= 1/1 - 1/4 + 1/4 - 1/7 + ... + 1/97 - 1/100
= 1 - 1/100 = 99/100
=> A = 33/100
8) A = 1/(4.7) + 1/(7.10) + ... + 1/(3n - 2)(3n + 1)
=> 3A = 3/(4.7) + 3/(7.10) + ... + 3/(3n - 2)(3n + 1)
= 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/(3n - 2) - 1/(3n + 1)
= 1/4 - 1/(3n + 1)
= (3n + 1 - 4) / 4(3n + 1)
= (3n - 3) / 4(3n + 1)
=> A = (n - 1) / 4(3n + 1)