Question

[Nguyễn Lê Tú Anh]

Rút gọn biểu thức

A = 1/2 + 1/2^2 + 1/2^3 +.......+1/2^100

Answer 1

[Hoàng Phúc]

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{100}}\)

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

=>\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\right)\)

=>\(A=1-\frac{1}{2^{100}}\)