1/2×5 + 1/5×8 + 1/8×11 + ......... + 1/2012×2015 = 1 - y:2/3
Vế trái:
1/2×5 + 1/5×8 + 1/8×11 + ......... + 1/2012×2015
= (3/3).(1/2×5 + 1/5×8 + 1/8×11 + ......... + 1/2012×2015)
= (1/3).(3/2×5 + 3/5×8 + 3/8×11 + ......... + 3/2012×2015)
= (1/3).(1/2 - 1/5 +1/5 - 1/8 +......+ 1/2012 - 1/2015)
= (1/3).(1/2 - 1/2015)
= 671/4030
Ta có: 671/4030 = 1 - y ÷ (2/3)
⇒ 671/4030 + 1 = -y÷(2/3)
⇒ 4701/4030 = -y÷(2/3)
⇒ -y = (4701/4030) × (2/3)
⇒ -y = 1567/2015
⇒ y = -1567/2015