Question

6+5^2+5^3+.....+5^1996=???

Answer 1

Đặt A=6+5²+5³+...+5¹⁹⁹⁶

=1+5+5²+5³+...+5¹⁹⁹⁶

=>5A=5+5²+5³+...+5¹⁹⁹⁷

=>5A-A=(5+5²+5³+...+5¹⁹⁹⁷)-(1+5+5²+...+5¹⁹⁹⁶)

=>4A=5¹⁹⁹⁷-1

\(\Rightarrow A=\frac{5^{1997}-1}{4}\)

Answer 2

\(A=6+5^2+5^3+...+5^{1996}\)

\(=1+5+5^2+...+5^{1996}\)

\(\Rightarrow5A=5+5^2+5^3+...+5^{1997}\)

\(\Rightarrow5A-A=4A=5^{1997}-1\)

\(\Rightarrow A=\frac{5^{1997}-1}{4}\)