Question

[Nguyễn Thế Thành Long]

Bài 1: Tính nhanh

5+5²⁺5³+......+5⁹⁸+5⁹⁹

^{Bài 2: Tìm x biết:}

a. [12x - 4] x 8²⁰²²= 4 x 8²⁰²³

Answer 1

[Thuỳ Linh Nguyễn]

Bài 1 :

Gọi \(A=5+5^2+5^3+...+5^{98}+5^{99}\\ 5A=5^2+5^3+5^4+...+5^{99}+5^{100}\\ 5A-A=\left(5^2+5^3+5^4+...+5^{99}+5^{100}\right)-\left(5+5^2+5^3+...+5^{98}+5^{99}\right)\\ 4A=5^{100}-5\\ A=\dfrac{5^{100}-5}{4}\)

Bài 2:

\(\left(12x-4\right)\cdot8^{2022}=4\cdot8^{2023}\\ 12x-4=4\cdot8^{2023}:8^{2022}\\ 12x-4=4\cdot8\\ 12x-4=32\\ 12x=36\\ x=3\)