Câu hỏi của Cute Vô Đối

Question

1.Tính

S= 1/3+ 1/3^2 + ... + 1/3^5000

Nguyễn Lê Phước Thịnh · Accepted Answer

$\dfrac{1}{3}S=\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{5001}}$

$\Leftrightarrow-\dfrac{2}{3}S=\dfrac{1}{3^{5001}}-\dfrac{1}{3}=\dfrac{1-3^{5000}}{3}$

$\Leftrightarrow S=\dfrac{1-3^{5000}}{3}:\dfrac{-2}{3}=\dfrac{1-3^{5000}}{-2}=\dfrac{3^{5000}-1}{2}$

Câu trả lời:

$\dfrac{1}{3}S=\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{5001}}$

$\Leftrightarrow-\dfrac{2}{3}S=\dfrac{1}{3^{5001}}-\dfrac{1}{3}=\dfrac{1-3^{5000}}{3}$

$\Leftrightarrow S=\dfrac{1-3^{5000}}{3}:\dfrac{-2}{3}=\dfrac{1-3^{5000}}{-2}=\dfrac{3^{5000}-1}{2}$