Question

Cho A = \(^{3^1+3^2+3^3+...+3^{2015}}\). Tìm n biết rằng: 2A + 3 =\(3^n\)

Answer 1

A = 3¹+3² + 3³+...3²⁰¹⁵

\(\Rightarrow\)3A= 3² + 3³+...+3²⁰¹⁶

^{\(\Rightarrow\)}2A = 3A -A = 3²⁰¹⁶ -3

\(\Rightarrow\)2A +3 = 3²⁰¹⁶

vậy n = 2016

Answer 2

Ta có :

      A= 3¹+3²+3³+3⁴+....+3²⁰¹⁵

=>3A= 3²+3³+3⁴+3⁵+....+3²⁰¹⁶

=>3A- A=(3²+3³+3⁴+3⁵+....+3²⁰¹⁶) - (3¹+3²+3³+3⁴+....+3²⁰¹⁵)

=>2A=3²⁰¹⁶-3

=>2A +3 =3²⁰¹⁶

Vậy n = 2016