Question

Rút gọn A= 1 + 5 + 5^2 + 5^ 3 + ... + 5^ 100

Answer 1

\(A=1+5+5^2+5^3+...+5^{100}\)

\(5A=5+5^2+5^3+...+5^{100}+5^{101}\)

\(5A-A=5+5^2+5^3+...+5^{100}+5^{101}-\left(1+5+5^2+5^3+...+5^{100}\right)\)

\(4A=5^{101}-1\)

\(A=\frac{5^{101}-1}{4}\)

Answer 2

A = 1+5+5²+5³+...+5¹⁰⁰

5A = 5+5²+5³+5⁴+....+5¹⁰¹

4A = 5A - A = 5¹⁰¹ - 1

=> A = \(\frac{5^{101}-1}{4}\)

Answer 3

thank you