Question

Cho A=5 + 5^2 + 5^3 + ......+ 5^2016

Tìm x biết : 4.A +5 = 5^x

MN giải hộ tui nha trình bày lun cũng dc toán nâng cao 

Answer 1

\(5A=5^2+5^3+5^4+...+5^{2017}\)

\(A=\frac{5A-A}{4}=\frac{5^{2017}-5}{4}=\frac{5\left(5^{2016}-1\right)}{4}\)

\(\Rightarrow4.A+5=\frac{4.5\left(5^{2016}-1\right)}{4}+5=5\left(5^{2016}-1\right)+5=5^x\)

\(\Rightarrow\frac{5\left(5^{2016}-1\right)}{5}+\frac{5}{5}=\frac{5^x}{5}\Rightarrow5^{2016}-1+1=5^{x-1}\)

\(\Rightarrow5^{2016}=5^{x-1}\Rightarrow x-1=2016\Rightarrow x=2017\)