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báo cáo

ai chat nhìu thì kt bn với mình nha

-27 nhá bạn

27 là dung

2 = 1 + 1     6 = 2 + 4     8 = 5 + 3     10 = 8 + 2

3 = 1 + 2     6 = 3 + 3     8 = 4 + 4     10 = 7 + 3

4 = 3 + 1     7 = 1 + 6     9 = 8 + 1     10 = 6 + 4

4 = 2 + 2     7 = 5 + 2     9 = 6+ 3     10 = 5 + 5

5 = 4 + 1     7 = 4 + 3     9 = 7 + 2     10 = 10 + 0

5 = 3 + 2     8 = 7 + 1     9 = 5 + 4     10 = 0 + 10

6 = 5 + 1     8 = 6 + 2     10 = 9 + 1     1 = 1 + 0

Tiếng  việt  khó .

\(10^{10}+\frac{1}{10}^{10}=10^{10}\)

\(10^9+\frac{1}{10}^8+1=10^9+1\)

\(10^{10}>10^9+1\)

Giải:

a) Gọi dãy đó là A, ta có:

\(A=\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2014}}\) 

\(2A=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2013}}\) 

\(2A-A=\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2013}}\right)-\left(\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2014}}\right)\) 

\(A=\dfrac{1}{2}-\dfrac{1}{2^{2014}}\) 

Vì \(\dfrac{1}{2}< 1;\dfrac{1}{2^{2014}}< 1\) nên \(\dfrac{1}{2}-\dfrac{1}{2^{2014}}< 1\) 

\(\Rightarrow A< 1\) 

b) \(A=\dfrac{10^{11}-1}{10^{12}-1}\) và \(B=\dfrac{10^{10}+1}{10^{11}+1}\) 

Ta có:

\(A=\dfrac{10^{11}-1}{10^{12}-1}\) 

\(10A=\dfrac{10^{12}-10}{10^{12}-1}\) 

\(10A=\dfrac{10^{12}-1+9}{10^{12}-1}\) 

\(10A=1+\dfrac{9}{10^{12}-1}\) 

Tương tự:

\(B=\dfrac{10^{10}+1}{10^{11}+1}\) 

\(10B=\dfrac{10^{11}+10}{10^{11}+1}\) 

\(10B=\dfrac{10^{11}+1+9}{10^{11}+1}\) 

\(10B=1+\dfrac{9}{10^{11}+1}\) 

Vì \(\dfrac{9}{10^{12}-1}< \dfrac{9}{10^{11}+1}\) nên \(10A< 10B\) 

\(\Rightarrow A< B\)

Ta có :

\(A=\dfrac{10^{11}-1}{10^{12}-1}< 1\)

\(\Leftrightarrow A< \dfrac{10^{11}-1+11}{10^{12}-1+11}=\dfrac{10^{11}+10}{10^{12}+10}=\dfrac{10\left(10^{10}+1\right)}{10\left(10^{11}+1\right)}=\dfrac{10^{10}+1}{10^{11}+1}=B\)

Vậy \(\dfrac{10^{11}-1}{10^{12}-1}< \dfrac{10^{10}+1}{10^{11}+1}\)

Vậy...

Vì \(10^{11}-1< 10^{12}-1\)

\(\Rightarrow\dfrac{10^{11}-1}{10^{12}-1}< \dfrac{10^{11}-1+11}{10^{12}-1+11}=\dfrac{10^{11}+10}{10^{12}+10}=\dfrac{10^{10}+1}{10^{11}+1}\)