\(\dfrac{-11}{-32}>\dfrac{16}{49}\)

\(\dfrac{-2020}{-2021}>\dfrac{-2021}{2022}\)

\(\dfrac{2021}{2022}=\dfrac{2020}{2021}\)

\(\dfrac{2021}{2022}\) và \(\dfrac{2020}{2021}\)

\(\dfrac{2021}{2022}=1-\dfrac{1}{2022}\)

\(\dfrac{2020}{2021}=1-\dfrac{1}{2021}\)

\(\text{Vì }\)\(\dfrac{1}{2022}>\dfrac{1}{2021}=>1-\dfrac{1}{2022}>1-\dfrac{1}{2021}=>\dfrac{2021}{2022}>\dfrac{2020}{2021}\)

2021/2022 > 2020/2021

Lời giải:

$6A=\frac{6^{2021}+6}{6^{2021}+1}=1+\frac{5}{6^{2021}+1}>1+\frac{5}{6^{2022}+1}$
$=\frac{6^{2022}+6}{6^{2022}+1}=6.\frac{6^{2021}+1}{6^{2022}+1}=6B$

$\Rightarrow A>B$

\(S^{2020}\)và\(S^{2021}\)?Thế này sai mất thui.

Vì \(2020< 2021\)nên\(S^{2020}< S^{2021}\).

sai đậm nha bạn

The Angry sai rồi

Nên chú ý rằng với một số \(S>0\)và \(m,n\in N,m>n\)thì:

Nếu \(0< S< 1\)thì \(S^m< S^n\)

Nếu \(S\ge1\)thì \(S^m\ge S^n\)

Bạn chưa chỉ ra khoảng giá trị của \(S\)thì không thể kết luận được.

Ta có : \(A.m=\frac{m\left(m^{2020+1}\right)}{m^{2021}-1}=\frac{m^{2021}+m}{m^{2021}-1}=1+\frac{m-1}{m^{2021}+1}\)

Tương tự ,ta có : \(B.m=1+\frac{m-1}{m^{2022}+1}\)

//Đề thiếu điều kiện của m nên không giải tiếp được =))

B = \(\dfrac{1}{2002}\) + \(\dfrac{2}{2021}\) + \(\dfrac{3}{2020}\)+...+ \(\dfrac{2021}{2}\) + \(\dfrac{2022}{1}\)

B = \(\dfrac{1}{2002}\) + \(\dfrac{2}{2021}\) + \(\dfrac{3}{2020}\)+...+ \(\dfrac{2021}{2}\) + 2022

B = 1 + ( 1 + \(\dfrac{1}{2022}\)) + ( 1 + \(\dfrac{2}{2021}\)) + \(\left(1+\dfrac{3}{2020}\right)\)+ ... + \(\left(1+\dfrac{2021}{2}\right)\) 

B = \(\dfrac{2023}{2023}\) + \(\dfrac{2023}{2022}\) + \(\dfrac{2023}{2021}\) + \(\dfrac{2023}{2020}\) + ...+ \(\dfrac{2023}{2}\) 

B = 2023 \(\times\) ( \(\dfrac{1}{2023}\) + \(\dfrac{1}{2022}\) + \(\dfrac{1}{2021}\) + \(\dfrac{1}{2020}\)+ ... + \(\dfrac{1}{2}\))

Vậy B > C 

\(2.A=\frac{2^{2021}-2}{2^{2021}-1}=1-\frac{1}{2^{2021}-1}\)

\(2B=\frac{2^{2022}-2}{2^{2022}-1}=1-\frac{1}{2^{2022}-1}\)

dó \(\frac{1}{2^{2022}-1}< \frac{1}{2^{2021}-1}\Rightarrow1-\frac{1}{2^{2022}-1}>1-\frac{1}{2^{2021}-1}\Rightarrow A< B\)

HT