Question

A=3+3^2+3^3+...+3^2004

a) CMR: A chia hết cho 130

b) A co la so chinh phuong khong ? tai sao?

Answer 1

a)A=3+3²+3³+...+3²⁰⁰⁴

=>3A=3²+3³+3⁴+...+3²⁰⁰⁵

=>3A-A=(3²+3³+3⁴+...+3²⁰⁰⁵)-(3+3²+3³+...+3²⁰⁰⁴)

=>2A=3²+3³+3⁴+...+3²⁰⁰⁵-3-3²-3³-...-3²⁰⁰⁴

=>2A=3²⁰⁰⁵-3

=>A=0,10025

Answer 2

\(A=3+3^2+3^3+...+3^{2004}\)

\(\Rightarrow3A=3^2+3^3+3^4+...+3^{2004}+3^{2005}\)

\(\Rightarrow3A-A=\left(3^2+3^3+3^4+...+3^{2004}+3^{2005}\right)-\left(3+3^2+3^3+...+3^{2004}\right)\)

\(\Rightarrow3A-A=2A=3^{2005}-3\)

\(\Rightarrow2A=3^{2005}-3\)

\(\Rightarrow A=\frac{3^{2005}-3}{2}\)

       Vậy \(A=\frac{3^{2005}-3}{2}\)