Question

cho biểu thức A=5+5^2+5^3+5^4+...+5^224

tìm n sao cho 4A+5=5^(n+1)^2

Answer 1

= 5

Answer 2

\(A=5+5^2+5^3+...+5^{224}\)

=>\(5A=5^2+5^3+5^4+...+5^{225}\)
=>\(5A-A=5^2+5^3+...+5^{225}-5-5^2-5^3-...-5^{224}\)

=>\(4\cdot A=5^{225}-5\)

=>\(4A+5=5^{225}\)

=>\(5^{\left(n+1\right)^2}=5^{225}\)

=>\(\left(n+1\right)^2=225\)

=>\(\left[{}\begin{matrix}n+1=15\\n+1=-15\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}n=14\\n=-16\end{matrix}\right.\)