Question

không quy đồng mẫu hãy tính tổng: S=1/2+1/2 mũ 2+1/2 mũ 3+...+1/2 mũ 2018

Answer 1

Ta có : 

\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2018}}\)

\(2S=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2017}}\)

\(2S-S=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2017}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2018}}\right)\)

\(S=1-\frac{1}{2^{2018}}\)

\(S=\frac{2^{2018}-1}{2^{2018}}\)

Vậy \(S=\frac{2^{2018}-1}{2^{2018}}\)

Chúc bạn học tốt ~