Question

Rút gọn biểu thức :

\(A=1+4+4^2+...+4^{90}\)

Answer 1

\(A=1+4+4^2+...+4^{90}\)

\(4A=4+4^2+4^3+...+4^{90}+4^{91}\)

\(4A-A=\left(4+4^2+4^3+...+4^{91}\right)-\left(1+4+4^2+...+4^{90}\right)\)

\(3A=4+4^2+4^3+...4^{91}-1-4-4^2-...-4^{90}\)

\(3A=4^{91}-1\)

\(A=\frac{4^{91}-1}{3}\)

t i c k nha ^^

Answer 2

4A= 4+4²+4³+....+4⁹¹

4a-4=(4+4²+4³+...+4⁹¹)-(1+4+4²+...+4⁹⁰)

3a=4⁹¹-1

a=(4⁹¹-1)/3

Answer 3

A = 1 + 4 + 4² + ... + 4⁹⁰

4A = 4 + 4² + 4³ + 4⁴  + ... + 4⁹¹

4A - A = 4 + 4² + 4³ + ... + 4⁹¹ - 1 - 4 - 4² - .. - 4⁹⁰

3A = 4⁹¹ - 1 => A = \(\frac{4^{91}-1}{3}\)

Answer 4

A = 1 + 4 + 4² + ... + 4⁹⁰

4A = 4 + 4² + 4³ + ... + 4⁹¹

4A - A = (4 + 4² + 4³ + ... + 4⁹¹) - (1 + 4 + 4² + ... + 4⁹⁰)

3A = 4⁹¹ - 1

A = \(\frac{4^{91}-1}{3}\)