Question

Cho A = 3¹ + 3² + 3³ + ... + 3²⁰⁰⁶

a) Thu gọn A

b) Tìm x để 2A + 3 = 3^x

Answer 1

a)3A=3(3¹ + 3² + 3³ + ... + 3²⁰⁰⁶)

3A=3²+3³+...+3²⁰⁰⁷

3A-A=(3²+3³+...+3²⁰⁰⁷)-(3¹ + 3² + 3³ + ... + 3²⁰⁰⁶)

2A=3²⁰⁰⁷-3

A=\(\frac{3^{2007}-3}{2}\)

b)2A+3=3^x

thay 2A=3²⁰⁰⁷-3 vào ta được

<=>3²⁰⁰⁷-3+3=3^x

<=>3²⁰⁰⁷=3^x

<=>x=2007

Answer 2

\(3A=3^2+3^3+3^4+...+3^{2007}\)

\(3A-A=2A=3^{2007}-3\)

\(A=\frac{3^{2007}-3}{2}\)

Answer 3

\(3A=3^2+3^3+3^4+...+3^{2007}\)

\(3A-A=2A=3^{2007}-3\)

\(A=\frac{3^{2007}-3}{2}\)

Answer 4

a) 3A=3²+3³+3⁴+...+3²⁰⁰⁷

3A-A=(3²+3³+3⁴+...+3²⁰⁰⁷)-(3¹+3²+3³+...+3²⁰⁰⁶)

2A=3²⁰⁰⁷-3

A=3²⁰⁰⁷-3/2

b) 2A+3=3^x

3²⁰⁰⁷-3+3=3^x

3²⁰⁰⁷=3^x

Suy ra x=2007