Question

Bài 1: Tính nhanh:

a) \(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{50}}\)

b)\(\dfrac{5}{3}+\dfrac{5}{3^2}+\dfrac{5}{3^3}+...+\dfrac{5}{3^{50}}\)

Answer 1

\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{50}}\)

\(3.A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{49}}\)

\(2A=3A-A=1-\dfrac{1}{3^{49}}\)

\(\Rightarrow A=\dfrac{1-\dfrac{1}{3^{50}}}{2}\)

\(B=\dfrac{5}{3}+\dfrac{5}{3^2}+...+\dfrac{5}{3^{50}}=5\left(\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{50}}\right)\)

Căn cứ vào câu A thì các trong ngặc bằng \(\dfrac{1-\dfrac{1}{3^{50}}}{2}\)

suy ra \(B=\dfrac{5\left(1-\dfrac{1}{3^{50}}\right)}{2}\)

tick mik nha

Answer 2

hoi kho day