Question

A=1+1/2+1/2^2+...+1/2^100 (và B=2) So sánh A và B

Answer 1

\(A=1+\frac{1}{2}+...+\frac{1}{2^{100}}\)

=>\(2A=2+1+\frac{1}{2}+...+\frac{1}{2^{99}}\)

=>2A-A=\(\left(2+1+\frac{1}{2}+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)=2-\frac{1}{2^{100}}

Answer 2

=> \(\frac{1}{2}\)A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{101}}\)

=> A - \(\frac{1}{2}\) A = \(\frac{1}{2}\)A = \(\frac{1}{2^{101}}-1\)

=> A = \(\frac{\frac{1}{2^{101}}-1}{2}=\frac{\frac{1}{2^{101}}}{2}-\frac{1}{2}=\frac{1}{2^{102}}-\frac{1}{2}

Answer 3

nhưng 2 - \(\frac{1}{2^{100}}\)= 2