Đáp án:
`=>196/197>196/(197+198)`
`=>197/198>197/(197+198`
`=>196/197+197/198>(196+197)/(197+198)`
`=>A>B`
Vậy `A>B`.
`B=1/4+1/5+1/6+...+1/19`
`=>B=1/4+(1/5+1/6...+1/9)+(1/10+1/11+...+1/19)`
Ta thấy `1/5>1/10;1/6>1/10;...;1/9>1/10`
`=>1/5+1/6+...+1/9>1/10+1/10+...+1/10` (Có `5` số hạng)
`=>1/5+1/6+...+1/10>1/2(1)`
Ta thấy `1/10>1/20;1/11>1/20;...;1/19>1/20`
`=>1/10+1/11+...+1/19>1/20+1/20+...+1/20` (Có `10` số hạng)
`=>1/10+1/11+...+1/19>1/2(1)`
Từ `(1)` và `(2)` ta có:
`=>1/4+1/5+1/6+...+1/19>1/2+1/2`
`=>1/4+1/5+1/6+...+1/19>1`
Vậy `B>1`.
