Question

cho A=3+3²+3³+.......+3²⁰¹⁶

a,Tính tổng A

b,tìm n để 2A+3=3ⁿ

^{nhanh lên nhé tớ đang càn gấp}

Answer 1

a) \(A=3+3^2+3^3+...+3^{2016}\)

\(\Rightarrow3A=3^2+3^3+3^4+...+3^{2017}\)

\(\Rightarrow3A-A=\left(3^2+3^3+3^4+...+3^{2017}\right)-\left(3+3^2+3^3+...+3^{2016}\right)\)

\(\Rightarrow2A=3^{2017}-3\)

\(\Rightarrow A=\frac{3^{2017}-3}{2}\)

b) \(2A+3=3^n\)

\(\Rightarrow2.\frac{3^{2017}-3}{2}+3=3^n\)

\(\Rightarrow3^{2017}-3+3=3^n\)

\(\Rightarrow3^{2017}=3^n\)

\(\Rightarrow n=2017\)

 

Answer 2

=3^1+3^2+3^3+....+3^2016

=[2016-1]:1+1.[2016+1]:2

=1008.2017=2033136

=3^2033136