$\text{Bài 4:}$
`a, A = 1/5 + 1/20 + 1/44 + 1/77 + ...+ 1/5252`
`⇒ A = 2/10 + 2/40 + 2/88 + 2/154 + ... + 2/10504`
`⇒ A = 2/2.5 + 2/5.8 + 2/8.11 + 2/11.14 +...+ 2/101.104`
`⇒ A = 2/3 . (3/2.5 + 3/5.8 + 3/8.11 + 3/11.14 +...+ 3/101.104)`
`⇒ A = 2/3 . (1/2 - 1/5 + 1/5 - 1/8 +...+ 1/101 - 1/104)`
`⇒ A = 2/3 . (1/2 - 1/104)`
`⇒ A = 1/3 - 1/156`
`⇒ A = 52/156 - 1/156 = 51/156`
`b, B = 2/3 + 14/15 + 34/35 + 62/63 + 98/99`
`⇒ B = (1 - 1/3) + (1 - 1/15) + (1 - 1/35) + (1 - 1/63) + (1 - 1/99)`
`⇒ B = (1 + 1 + 1 + 1 + 1) - (1/3 + 1/15 + 1/35 + 1/63 + 1/99)`
`⇒ B = 5 - (1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11)`
`⇒ B = 5 - 1/2 . (2/1.3 + 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11)`
`⇒ B = 5 - 1/2 . (1 - 1/3 + 1/3 - 1/5 + ... + 1/9 - 1/11)`
`⇒ B = 5 - 1/2 . (1 - 1/11)`
`⇒ B = 5 - 1/2 . 10/11`
`⇒ B = 5 - 5/11 = 50/11`
