Question

a=3¹+3²+........3²⁰⁰⁶

a) tìm a

b) tìm x biết 2a +3=3^x

 

Answer 1

=>3a=3²+3³+...+3²⁰⁰⁷

=>3a-a=2a=(3²+3³+3⁴+...+3²⁰⁰⁷)-(3+3²+...+3²⁰⁰⁶)

=>2a=3²⁰⁰⁷-3

=>2a+3=3²⁰⁰⁷-3+3

=>3^x=3²⁰⁰⁷

=>x=2007

Answer 2

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

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

\(3A-A=\left(3^2+3^3+...+3^{2007}\right)-\left(3+3^2+...+3^{2006}\right)\)

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

=> 2a +3=3²⁰⁰⁷ - 3 + 3 = 3²⁰⁰⁷ = 3^x

=> x = 2007