Question

[pham duc hai]

giup bai 1 2

Answer 1

[Akai Haruma]

1a.

\(A=\frac{2}{3}+\frac{4}{9}+\frac{2}{7}-\frac{7}{5}+\frac{1}{21}-\frac{2}{45}+4\frac{2015}{2016}\)

\(=(\frac{2}{3}+\frac{2}{7}+\frac{1}{21})+(\frac{4}{9}-\frac{7}{5}-\frac{2}{45})+4\frac{2015}{2016}\)

\(=\frac{14+6+1}{21}+\frac{20-63-2}{45}+4\frac{2015}{2016}=1-1+4\frac{2015}{2016}=4\frac{2015}{2016}\)

1b.

\(B=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+....+\frac{6}{87.90}=2(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+....+\frac{3}{87.90})\)

\(=2\left(\frac{18-15}{15.18}+\frac{21-18}{18.21}+\frac{24-21}{21.24}+....+\frac{90-87}{87.90}\right)\)

\(=2\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+....+\frac{1}{87}-\frac{1}{90}\right)=2(\frac{1}{15}-\frac{1}{90})=\frac{1}{9}\)

Answer 2

[Akai Haruma]

1c.

\(C=\frac{20.2^4+12.2^4-48.2^2}{8^2}=\frac{20.2^4+12.4.2^2-48.2^2}{8^2}=\frac{20.2^4+48.2^2-48.2^2}{8^2}=\frac{20.2^4}{8^2}=5\)

1d.

\(D=1-5+9-13+17-21+....+169-173\)

\(=(1-5)+(9-13)+(17-21)+...+(169-173)\)

\(=\underbrace{(-4)+(-4)+(-4)+....+(-4)}_{22}=(-4).22=-88\)

1e.

\(E=1.2+2.3+3.4+4.5+...+216.217\)

\(3E=1.2.3.+2.3.3+3.4.3+4.5.3+....+216.217.3\)

\(=1.2.3+2.3(4-1)+3.4(5-2)+4.5(6-3)+...+216.217(218-215)\)

\(=(1.2.3+2.3.4+3.4.5+...+216.217.218)-(1.2.3+2.3.4+3.4.5+...+215.216.217)\)

\(=216.217.2018\)

\(\Rightarrow E=72.217.218\)