Câu hỏi của Origami Đăng Khôi

Question

Tính nhanh tổng sau:

B=1/3+1/9+1/27+...+1/2187+1/6561

Giúp mik với huhu :((((

HT.Phong (9A5) · Accepted Answer

$B=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{2187}+\dfrac{1}{6561}$

$3B=3\cdot\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{6561}\right)$

$3B=1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}+\dfrac{1}{2187}$

$3B-B=\left(1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{6561}\right)$

$2B=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+\left(\dfrac{1}{9}-\dfrac{1}{9}\right)+...+\left(1-\dfrac{1}{6561}\right)$

$2B=0+0+...+1-\dfrac{1}{6561}$

$2B=1-\dfrac{1}{6561}$

$B=\left(1-\dfrac{1}{6561}\right):2$

$B=\dfrac{6560}{6561}:2$

$B=\dfrac{3280}{6561}$Câu trả lời: $B=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{2187}+\dfrac{1}{6561}$