Question

Tính tổng:

S= 1/3 + 1/3² + 1/3³ +....+ 1/3⁸ + 1/ 3⁹

GIẢI TỪNG BƯỚC RA GIÚP MK VS. MK SẼ TICK.

Answer 1

\(S=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}+\frac{1}{3^9}\)

\(\Rightarrow3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}+\frac{1}{3^8}\)

\(\Rightarrow3S-S=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}+\frac{1}{3^8}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}+\frac{1}{3^9}\right)\)

\(\Rightarrow2S=1-\frac{1}{3^9}\)

\(\Rightarrow S=\frac{1-\frac{1}{3^9}}{2}\)

Answer 2

thế nào vậy