\(A\cdot\left(1-\frac{1}{2}\right)=\left(1-\frac{1}{2}\right)\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)=1-\frac{1}{2^{2013}}\)

\(\Rightarrow A=2\cdot\left(1-\frac{1}{2^{2013}}\right)=2-\frac{1}{2^{2012}}\)

Cũng có cách khác như sau:

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

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

Cứ đuổi dần từ đuôi lên 

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

=(4x5x7x888x8+48936637x28674389232698)x0

=0

\(\sqrt{x}=\sqrt{5}\Rightarrow x=5\)

\(\sqrt{x}=0\Rightarrow x=0\)

a)5^x+2=625

<=>5^x+2=5⁴

<=>x+2=4

<=>x=2