Question

Cho A = \(\dfrac{1}{2}\) + \(\dfrac{1}{2^{2}}\)+ \(\dfrac{1}{2^{3}}\)+ \(\dfrac{1}{2^{4}}\) + ...+ \(\dfrac{1}{2^{10}}\)

Chứng tỏ rằng A + \(\dfrac{1}{2^{10}}\)= 1

Answer 1

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{2\cdot2}+\dfrac{1}{2\cdot2}-\dfrac{1}{2\cdot2\cdot2}+\dfrac{1}{2\cdot2\cdot2}-\dfrac{1}{2\cdot2\cdot2\cdot2}+.....+\dfrac{1}{2^{10}}\)

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

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