Câu hỏi của vo xuan sang

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

Nguyễn Thanh Hằng · Accepted Answer

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 ~Câu trả lời: 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 ~

vo xuan sang · Answer

minh ko hiểu chỗ 2A -A đến hếtCâu trả lời: minh ko hiểu chỗ 2A -A đến hết