Đáp án:
$\text{Bạn tham khảo nhé!}$
Giải thích các bước giải:
`1`
`A=196/197+197/198` và `B=(196+197)/(197+198)`
Ta có:
`196/197>196/(197+198)`
`197/198>197/(197+198)`
`=>196/197+197/198>(196+197)/(197+198)`
`=>A>B`.
`2`
Ta có `1/4+1/5+1/6+...+1/19`
`=1/4+(1/5+1/6+...+1/9)+(1/10+1/11+...+1/19)`
Ta thấy `1/5>1/9;1/6>1/9;1/7>1/9;1/8>1/9`
`=>1/5+1/6+...+1/9>1/9+1/9+...+1/9` (Có `5` số hạng)
`=>1/5+1/6+...+1/9>5/9>1/2``(1)`
Ta thấy `1/10>1/19;1/11>1/19;1/12>1/19;...;1/18>1/19`
`=>1/10+1/11+...+1/19>1/19+1/19+...+1/19` (Có `10` số hạng)
`=>1/10+1/11+...+1/19>10/19>1/2``(2)`
Từ `(1)` và `(2)` ta có:
`=>1/5+1/6+...+1/19>5/9+10/19>1/2+1/2=1`
`=>1/5+1/6+...+1/19>1`
`=>1/4+1/5+1/6+...+1/19>1`
Vậy `B>1`.
`3`
$M=\dfrac{\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{3}{11}}{\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{11}}$
$⇒M=\dfrac{\dfrac{3}{4}(\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{11})}{\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{11}}$
$⇒M=\dfrac{3}{4}$
Vậy `M=3/4`.
`4`
`S=3/1.4+3/4.7+3/7.10+...+3/40.43+3/43.46`
`S=1-1/4+1/4-1/7+1/7-1/10+...+1/40-1/43+1/43-1/46`
`S=1-1/46<1`
Vậy `S<1`.
`5`
`B=1/2^2+1/3^2+1/4^2+...+1/8^2`
`B=1/2.2+1/3.3+1/4.4+...+1/8.8`
`B<1/1.2+1/2.3+1/3.4+...+1/7.8`
`B<1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8`
`B<1-1/8<1`
Vậy `B<1`.