Question

[ARMY]

M==1+1/2+1/2^2+1/2^3+....+1/2^2016

So sanh M voi 2

Answer 1

[Không Tên]

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

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

\(\Rightarrow\)\(2M-M=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)\)

\(\Rightarrow\)\(M=2-\frac{1}{2^{2016}}< 2\)

Vậy  M < 2