Đáp án:

Giải thích các bước giải:

`5`.

`A=5/4.6+5/6.8+5/8.10+...+5/298.300`

`=>A/5=1/4.6+1/6.8+1/8.10+...+1/298.300`

`=>(2A)/5=2/4.6+2/6.8+2/8.10+...+2/298.300`

`=>(2A)/5=1/4-1/6+1/6-1/8+1/8-1/10+...+1/298-1/300`

`=>(2A)/5=1/4-1/300`

`=>(2A)/5=37/150`

`=>2A=37/150*5`

`=>2A=37/30`

`=>A=37/30:2`

`=>A=37/60`

Vậy biểu thức có giá trị là `37/60`.

`6`.

`=>text(A)=(2011^2011+2)/(2011^2011-1`

`=>text(A)=(2011^2011-1+3)/(2011^2011-1`

`=>text(A)=(2011^2011-1)/(2011^2011-1)+3/(2011^2011-1)`

`=>text(A)=1+3/(2011^2011-1`

`=>text(B)=(2011^2011)/(2011^2011-3`

`=>text(B)=(2011^2011-3+3)/(2011^2011-3`

`=>text(B)=(2011^2011-3)/(2011^2011-3)+3/(2011^2011-3)`

`=>text(B)=1+3/(2011^2011-3)`

`=>2011^2011-1>2011^2011-3`

`=>3/(2011^2011-1)<3/(2011^2011-3)`

`=>1+3/(2011^2011-1)<1+3/(2011^2011-3)`

`=>text(A)<text(B)`

Vậy `text(A) < text(B)`.

Đáp án:

$\\$

Bài `5.`

`5/(4×6) + 5/(6×8) + ... + 5/(298 × 300)`

`= 5 × [1/(4×6) + 1/(6×8) + ... + 1/(298 × 300)]`

`= 5 × 1/2 × [1/4 - 1/6 + 1/6 - 1/8 + ... + 1/298 - 1/300]`

`= 5/2 × [1/4 + (-1/6 + 1/6) + ... + (-1/298 + 1/298) - 1/300]`

`= 5/2 × [1/4 - 1/300]`

`= 5/2 × [75/300 - 1/300]`

`= 5/2 × 37/150`

`= 37/60`

$\\$

Bài `6.`

`A = (2011^{2011} + 2)/(2011^{2011} - 1)`

`-> A = (2011^{2011} - 1 + 3)/(2011^{2011} - 1)`

`-> A = (2011^{2011} - 1)/(2011^{2011}-1) + 3/(2011^{2011} -1)`

`-> A =1 + 3/(2011^{2011} - 1)`

`B = 2011^{2011}/(2011^{2011}-3)`

`-> B = (2011^{2011} -3+3)/(2011^{2011}-3)`

`-> B = (2011^{2011}-3)/(2011^{2011-3) + 3/(2011^{2011} - 3)`

`-> B = 1 + 3/(2011^{2011} - 3)`

Vì : `-1 > -3`

`-> 2011^{2011} - 1 > 2011^{2011} - 3`

`-> 1/(2011^{2011}- 1) < 1/(2011^{2011}-3)`

`-> 3/(2011^{2011}-1) < 3/(2011^{2011} - 3)`

`-> 1 + 3/(2011^{2011} - 1) <  1 + 3/(2011^{2011} - 3)`

`-> A < B`

Vậy `A < B`