Question

Tính nhanh:

a)4⁵ . 9⁴ - 2 . 6⁹/ 2¹⁰ . 3⁸ + 6⁸ . 20

b)2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ +...+ 2² - 2

c)(1+1/3+1/5+...+1/99) : (1/1.99+1/3.97+...+1/99.1)

(dấu chấm là dấu nhân nha). Cảm ơn mn

Answer 1

a)\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(3.2\right)^8.2^2.5}=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+3^8.2^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+3^8.2^{10}.5}\)

\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=\frac{-2}{6}=\frac{-1}{3}\)

b) đặt A=2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ +...+ 2² - 2

=>2A=2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+...+2³-2²

=>2A+A=2¹⁰¹-2¹⁰⁰+2⁹⁹-2⁹⁸+...+2³-2²+2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ +...+ 2² - 2

=>3A=2¹⁰¹-2

=>A=\(\frac{2^{101}-2}{3}\)

Answer 2

thank kiu 

thank kiu

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Answer 3

Thank you bạn trieu dang