$a$) Ta có:
`VP = 1/n - 1/{n+a} = {(n+a)}/{n.(n+a)} - n/{n.(n+a)} = {n+a-n}/{n.(n+a)} = a/{n.(n+a)} = VT` ($đ.p.c.m$)
$b$)
`A = 1/15 + 1/35 + .... + 1/2499`
`⇔ A = 1/{3.5} + 1/{5.7} + ..... + 1/{49.51}`
`⇔ 2A = 2/{3.5} + 2/{5.7} + .... + 2/{49.51}`
`⇔ 2A = 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/49 - 1/51`
`⇔ 2A = 1/3 - 1/51`
`⇔ 2A = 16/51`
`⇔ A = 8/51`
`B = 3/{5.8} + 11/{8.19} + 12/{19.31} + {70}/{31.101} + 99/{101.200}`
`⇔ B = 1/5 - 1/8 + 1/8 - 1/19 + 1/19 - 1/31 + 1/31 - 1/101 - 1/101 - 1/200`
`⇔ B = 1/5 - 1/200`
`⇔ B = 39/200`