Question

rút gọn 

1+5+5^2+...........+5^100

Answer 1

\(1+5+5^2+...5^{100.}\)

\(=1+5+5^{2+...+100}\)

\(=1+5+5^{99}\)

\(=1+5^1+5^{99}\)

\(=1+5^{1+99}\)

\(=1+5^{100}\)

\(=1+500\)

\(=501\)

Answer 2

Vậy, 5A = 5¹ + 5² + 5³ +... + 5⁵⁰ + 5⁵¹. 

5A - A = 4A = (5¹ + 5² + 5³ +... + 5⁵⁰) + 5⁵¹ - 5⁰ + (5¹ + 5² + 5³ +... + 5⁴⁹ + 5⁵⁰) = 5⁵¹ - 1. 

Tức, A = \(\frac{\left(5^{51}-1\right)}{4}\)