Question

1/2+1/22+1/23+1/24+.............+1/210

Answer 1

Sửa đề: \(\frac12+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\cdots+\frac{1}{2^{10}}\)

Đặt \(A=\frac12+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\cdots+\frac{1}{2^{10}}\)

=>\(2A=1+\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^9}\)

=>\(2A-A=1+\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^9}-\frac12-\frac{1}{2^2}-\cdots-\frac{1}{2^{10}}\)

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