Question

1+1/3+1/3^2+1/3^3+1/3^4+.... .+1/3^n

        CÁC BẠN GIÚP MÌNH VS NHÉ MAI MÌNH                                PHẢI NỘP RỒI😊😊😊😊​

Answer 1

đặt \(A=1+\frac{1}{3}+\frac{1}{3^2}+.....+\frac{1}{3^n}\)

\(\Rightarrow3A=3+1+\frac{1}{3}+...+\frac{1}{3^{n-1}}\)

\(\Rightarrow3A-A=(3+1+...+\frac{1}{3^{n-1}})-(1+\frac{1}{3}+...+\frac{1}{3^n})\)

\(\Rightarrow2A=3-\frac{1}{3^n}\)

\(\Rightarrow A=(3-\frac{1}{3^n})\div2\)

Answer 2

Đặt A=1 + 1/3 + 1/3² + 1/3³⁺...+  1/3ⁿ

=>  3A= 3 + 1 + 1/3 + 1/3² +...+ 1/3^n-1

=>   3A - A = 2A = 3 - 1/3ⁿ

=> 2A =(3ⁿ⁺¹ - 1) / 3ⁿ

=> A= (3ⁿ⁺¹ - 1) / 3ⁿ.2

K cho mk nha!