Question

tinh tong sau :

A= 1/2 +1/2^2+1/2^3+...+ 1/2^2015+1/2^2016

Answer 1

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.......+\frac{1}{2^{2015}}\)

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

=>\(A=1-\frac{1}{2^{2016}}\)

=>\(A=\frac{2^{2016}-1}{2^{2016}}\)

Answer 2

Ta có : \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2016}}\)

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+......+\frac{1}{2^{2016}}\)

\(\Rightarrow2A-A=1-\frac{1}{2^{2016}}\)

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

Answer 3

ta có : 2A = 2 . ( 1 + 1/2^2 + 1/2^3 + ... + 1/2^2016 )

= 1 + 1/2 + 1/2^2 + ... + 1/2^2017

=>2A - A = (1 + 1/2 + 1/2^2 + ... + 1/2^2015 ) - ( 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^2016 )

=1 - 1/2^2016 = 2^2016 - 1/2^2016

đến đây ko tính được nữa, bạn cứ dữ đáp án này là được!