Đáp án:
$\\$
`M = 2/(3×5) + 2/(5×7) + ... + 2/(9×13)`
`-> M = 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/9 - 1/13`
`->M = 1/3 + (-1/5 + 1/5) + ... + (-1/9 + 1/9) - 1/13`
`->M = 1/3 - 1/13`
`->M = 13/39 - 3/39`
`-> M = 10/39`
Vậy `M=10/39`
$\\$
`N = 4/(2×4) + 4/(4×6) + ... + 4/(2014 × 2016)`
`-> N = 4 × [1/(2×4) + 1/(4×6) + ... + 1/(2014 × 2016)]`
`-> N = 4 × 1/2 × [1/2 - 1/4 + 1/4 - 1/6 + ... + 1/2014 - 1/2016]`
`-> N = 2 × [1/2 + (-1/4 + 1/4) + ... + (-1/2014 + 1/2014) - 1/2016]`
`-> N = 2 × [1/2 - 1/2016]`
`-> N = 2 × [1008/2016 - 1/2016]`
`-> N = 2 × 1007/2016`
`-> N = 1007/1008`
Vậy `N=1007/1008`
