Question

Cho A= 1/2+1/2^2+1/2^3+1/2^4+......+1/2^10

Chứng tỏ rằng A + 1/2^10 = 1

Answer 1

\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+.......+\dfrac{1}{2^{10}}\)

\(\Leftrightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^9}\)

\(\Leftrightarrow2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\right)\)

\(\Leftrightarrow A=1-\dfrac{1}{2^{10}}\)

\(\Leftrightarrow A+\dfrac{1}{2^{10}}=1\left(đpcm\right)\)

Answer 2

1+1=3