Question

Rút gọn 

A = 1 + 5 + 5^2 + 5^3 + 5^3 + ...+ 5^49 + 5^50

Answer 1

A = 1 + 5 + 5² + 5³ + 5³ + ...+ 5⁴⁹ + 5⁵⁰

5A = 5(5⁰+5¹+5²+5³+...+5⁴⁹+5⁵⁰)

5A=5¹+5²+5³+5⁴+...+5⁵⁰+5⁵¹

5A-A=(5¹+5²+5³+5⁴+...+5⁵⁰+5⁵¹)-(5⁰ + 5¹ + 5² + 5³ + 5³ + ...+ 5⁴⁹ + 5⁵⁰)

4A=5⁵¹-1

A=(5⁵¹-1):4

Answer 2

5A = 5 + 5^2 + 5^3 + 5^4 + 5^5 +...+ 5^50 + 5^51

=> 4A = ( 5 + 5^2 + 5^3 + 5^4 + 5^5 +...+ 5^50 + 5^51 ) - ( 1 + 5 + 5^2 + 5^3 +...+ 5^49 + 5^50 )

=> 4A = 5^51 - 1

=> A = \(\frac{5^{51}-1}{4}\)