Đáp án:
A = 2018 + ( 2016/2017 + 1009/2020) :2
Giải thích các bước giải:
A= ( 1+ 1/1.3)+ ( 1+ 1/2.4)+....+ (1+ 1/2018. 2020)
A= (1+ 1+ 1+ 1+...+1) + ( 1/1.3+ 1/2.4+ 1/3.5 + ....+ 1/2028.2020)
Đặt 1/1.3+ 1/2.4+ 1/3.5 + ....+ 1/2028.2020 = B
Ta có:
B = 1/1.3+ 1/2.4+ 1/3.5 + ....+ 1/2018.2020
B= ( 1/1.3+ 1/3.5 +...+ 1/2017. 2019) + ( 1/2.4+ 1/4.6+...+ 1/2018.2020)
2. B = 2. ( 1/1.3+ 1/3.5+...+ 1/2017. 2019) + 2. ( 1/2.4+ 1/4.6+...+ 1/2018.2020)
2.B = ( 2/1.3+ 2/3.5+....+ 2/2017. 2019) + ( 2/2.4 + 2/4.6+...+ 2/2018.2020)
2.B = ( 1- 1/3+ 1/3- 1/5+.....+ 1/2017-1/2019) + ( 1/2 - 1/4+ 1/4 - ... + 1/2018 - 1/2020)
2.B = ( 1- 1/2017) + ( 1/2- 1/2020)
2.B = 2016/2017 + 1009/2020
B = ( 2016/2017 + 1009/2020) : 2
⇒ A = 2018 + ( 2016/2017 + 1009/2020) :2
Nhớ kiểm tra lại nhé, học tốt!
