Question

Cho \(B=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\) . Chứng minh rằng: \(B< 1\)

Help me! Đề thi toán học kì II!

Answer 1

\(B=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\)

\(\Rightarrow2B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\)

\(\Rightarrow2B-B=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)=1-2^{2016}< 1\)

=>đpcm

Answer 2

mìk ko chắc

Answer 3

Cảm ơn bạn Đào Nguyên Nhật Hạ nhiều nha

Answer 4

ko có gì đâu!