Giải thích các bước giải:
a, A=2/1.3 + 2/3.5 + 2/5.7 + 2/7.9+....+ 2/2017.2019
= 2. (1/1.3 + 1/3.5 +1/5.7 + 1/7.9+....+ 1/2017.2019 )
= 2. (1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+....+1/2017-1/2019)
= 2. (1-1/2019)
= 2.2018/2019
= $\frac{4036}{2019}$
b, 1/31+ 1/32+ 1/33....+ 1/60
(1/31+ 1/32+ 1/33+...+1/40) + (1/41+ 1/42+ 1/43+...+1/50) + (1/51+ 1/52+ 1/53+...+1/60)
Ta tha'y :
1/31+ 1/32+ 1/33+...+1/40 < 1/3
1/41+ 1/42+ 1/43+...+1/50 < 1/4
1/51+ 1/52+ 1/53+...+1/60 < 1/5
⇒ S = 1/3+1/4+1/5
⇒ 47/60 < $\frac{4}{5}$
Hay 47/60 < $\frac{4}{5}$
Xin cau tra loi hay nhat.
