Question

1. Tính bằng cách hợp lý

a) \(\frac{-1}{5}\cdot\frac{6}{7}+\frac{3}{7}\cdot\frac{3}{5}+\frac{2^5\cdot27}{3^3\cdot64}\)

b) S = \(2+2^2+2^3+...+2^9\)

Answer 1

b, S = 2 + 2² + 2³ + ...+2⁹.

2S = 2(2 + 2² + 2³ + ... + 2⁹).

= 2² + 2³ + 2⁴ + ... + 2¹⁰.

2S - S = (2² + 2³ + 2⁴ + ... + 2¹⁰) - (2 + 2² + 2³ + ... + 2⁹).

S = 2¹⁰ - 2.

Vậy S = 2¹⁰ - 2.

~Chúc bn học tốt!!!~

Answer 2

a, \(\dfrac{-1}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}+\dfrac{2^5.27}{3^3.64}.\)

\(=\dfrac{-1}{5}.\dfrac{3}{7}.2+\dfrac{3}{7}.\dfrac{3}{5}+\dfrac{32.27}{27.64}.\)

\(=\dfrac{3}{7}\left(\dfrac{-1}{5}.2+\dfrac{3}{5}\right)+\dfrac{2.1}{1.2}.\)

\(=\dfrac{3}{7}.\dfrac{1}{5}+1.\)

\(=\dfrac{3}{35}+1.\)

\(=\dfrac{3}{35}+\dfrac{35}{35}.\)

\(=\dfrac{38}{35}.\)

~Chúc bn học tốt!!!~