Question

Tính \(M=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+..........+\dfrac{1}{2^{2011}}+\dfrac{1}{2^{2012}}\)

Nguyễn NamTrần Quốc LộcNguyễn Thanh HằngTrần Hoàng NghĩaRibi Nlê thị hương giangkok NgokAkai HarumaAce Legona

Answer 1

\(\)\(M=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2011}}+\dfrac{1}{2^{2012}}\)

\(2M=2\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2011}}+\dfrac{1}{2^{2012}}\right)\)

\(2M=1+\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{2010}}+\dfrac{1}{2^{2011}}\)

\(2M-M=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2010}}+\dfrac{1}{2^{2011}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2011}}+\dfrac{1}{2^{2012}}\right)\)

\(M=1-\dfrac{1}{2^{2012}}\)