Question

A=6+5²+5³+5⁴+...+5¹⁹⁹⁶+5¹⁹⁹⁷

^{Tính giá trị biểu thức đó}

Answer 1

A=6+5²+5³+5⁴+...+5¹⁹⁹⁶+5¹⁹⁹⁷

A = 1 + 5 + 5² + 5³ + ... + 5¹⁹⁹⁶ + 5¹⁹⁹⁷

5A = 5 + 5² + 5³ + 5⁴ + ... + 5¹⁹⁹⁷ + 5¹⁹⁹⁸

5A - A = ( 5 + 5² + 5³ + 5⁴ + ... + 5¹⁹⁹⁷ + 5¹⁹⁹⁸ ) - ( 1 + 5 + 5² + 5³ + ... + 5¹⁹⁹⁶ + 5¹⁹⁹⁷ )

4A = 5¹⁹⁹⁸ - 1

\(\Rightarrow A=\frac{5^{1998}-1}{4}\)

Answer 2

\(A=6+5^2+5^3+...+5^{1996}+5^{1997}\\ A=1+5+5^2+5^3+...+5^{1996}+5^{1997}\)

\(5A=5+5^2+5^3+...+5^{1996}+5^{1998}\)

\(5A-A=\left(5+5^2+5^3+...+5^{1996}+5^{1998}\right)-\left(1+5+5^2+5^3+...+5^{1996}+5^{1997}\right)\)

\(4A=5^{1998}-1\\ A=\frac{5^{1998}-1}{4}\)