Question

Tính tổng sau:
A=1/2+1/2^2+1/2^3+...+1/2015^2015+1/2016^2016

giúp mình nha cần gấp hiuhiu

Answer 1

Ta có :

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

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

\(\Rightarrow2A-A=\left(1+\dfrac{1}{2}+..........+\dfrac{1}{2^{2015}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+.......+\dfrac{1}{2^{2016}}\right)\)

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

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

~ Học tốt ~