a/ \(\left|5x+\frac{3}{4}\right|-\frac{5}{4}=2\)

\(\left|5x+\frac{3}{4}\right|=\frac{13}{4}\)

\(\Rightarrow x=\left\{\frac{1}{2};-\frac{4}{5}\right\}\)

b/\(\frac{3}{2}-\left|\frac{1}{2}x+1\right|=\frac{1}{4}\)

\(\left|\frac{1}{2}x+1\right|=\frac{5}{4}\)

1/\(\frac{1}{2}x+1=\frac{5}{4}\)
\(\frac{1}{2}x=\frac{1}{4}\)
\(x=\frac{1}{2}\)

2/\(\frac{1}{2}x+1=-\frac{5}{4}\)

\(\frac{1}{2}x=-\frac{9}{4}\)

\(x=-\frac{9}{2}\)​

\(\Rightarrow x=\left\{\frac{1}{2};-\frac{9}{2}\right\}\)

\(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

\(A=2-\frac{1}{2^{2012}}\)

k nha

Nhân 2A lên rồi lấy 2A-A là ra kết quả

\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

\(\Rightarrow A=2A-A\)

\(\Rightarrow A=2-\frac{1}{2^{2012}}\)

Sai đề không bạn?

1/2+1/3+1/4=5/6+1/4

=13/12

13/12

 Tick cho mik nha!!!

quy đồng lên là làm được thôi

ban giup minh di. giai day du cho minh di

Ta có: (a-b)² (a+b)>=0
=> (a-b)(a²-b²) >=0 
=> a ³ +b³- a²b -ab² >=0
=> 3a³+3b³-3a²b-3ab²>=0
=> 4a³+4b³>= (a^3+b^3+3a²b+3ab²)
=> 4a³+ 4b³ >=  (a+b)³ => đpcm, tích cho mình nhé

1-1/2+1/3-1/4+...+1/199-1/200=(1+1/2+1/3+1/4+...+199+1/200)-(1+1/2+1/3+...+1/100)=1+1/2+1/3+1/4+...+1/199+1/200-1-1/2-1/3-1/4-...-1/99-1/100=(1+1/2+1/3+...+1/100)-(1+1/2+1/3+...+1/100)+(1/101+1/102+...+1/200)=0+(1/101+1/102+...+1/200)=(1/101+1/102+...+1/200)(đpcm)

\(\frac{1}{\sqrt{a}+\sqrt{a+1}}=\frac{\sqrt{a+1}-\sqrt{a}}{\left(\sqrt{a}+\sqrt{a+1}\right)\left(\sqrt{a+1}-\sqrt{a}\right)}=\frac{\sqrt{a+1}-\sqrt{a}}{a+1-a}=\sqrt{a+1}-\sqrt{a}\Rightarrow\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.......+\frac{1}{\sqrt{99}+\sqrt{100}}=-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-......-\sqrt{99}+\sqrt{100}=10-1=9\)