Câu hỏi của Phùng Anh Đức 6a5

Question

1/2-1/2²+1/ 2³-1/2⁴+...+1/2⁹⁹-1/2¹⁰⁰

help me !!!!!!! cần gấp lắm .

✎✰ ๖ۣۜLαɗσηηα ༣✰✍ · Accepted Answer

Đặt $A=\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}$

$2A=1-\frac{1}{2}+...+\frac{1}{2^{98}}-\frac{1}{2^{99}}$

$2A+A=\left(1-\frac{1}{2}+...+\frac{1}{2^{98}}-\frac{1}{2^{99}}\right)+\left(\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\right)$

$3A=1-\frac{1}{2^{100}}$

$A=\frac{1-\frac{1}{2^{100}}}{3}$

hok tốt!!

Câu trả lời:

Đặt $A=\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}$

$2A=1-\frac{1}{2}+...+\frac{1}{2^{98}}-\frac{1}{2^{99}}$

$2A+A=\left(1-\frac{1}{2}+...+\frac{1}{2^{98}}-\frac{1}{2^{99}}\right)+\left(\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\right)$

$3A=1-\frac{1}{2^{100}}$

$A=\frac{1-\frac{1}{2^{100}}}{3}$

hok tốt!!