Question

Cho A= \(3^1+3^2+3^{3+...+3^{2006}}\)

a/ thu gọn A

b/ tìm x để 2A+3=3\(^x\)

Answer 1

A = 3¹+3²+3³+.....+3²⁰⁰⁶

3A = 3²+3³+3⁴+....+3²⁰⁰⁷

2A = 3A - A = 3²⁰⁰⁷-3

=> A = \(\frac{3^{2007}-3}{2}\)

Vì 2A = 3²⁰⁰⁷-3

=> 2A + 3 = 3²⁰⁰⁷

Mà 2A + 3 = 3^x

=> 3^x = 3²⁰⁰⁷

=> x = 2007