A = 2 x 100 - 2 x 99 + 2 x 98 - 2 x 97 + ... + 2 x 2 - 2x 1

Xét dãy số: 1; 2;...;97; 98; 99; 100

Dãy số trên có 100 số hạng. Vì 100 : 2 = 50

Nhóm hai số hạng liên tiếp của a vào một nhóm khi đó ta có:

A = (2 x 100 - 2 x 99) + (2 x 98 - 2 x 97) +...+(2x2 - 2 x1)

A = 2 x (100 - 99) + 2 x (98 - 97) + ...+ 2 x (2 - 1)

A = 2 x 1 + 2 x 1 + ... + 2 x 1

A = 2 + 2 + ... + 2

A = 2 x 50

A = 100

4 boys, 3 girls

M=\(\dfrac{8}{15}\)

\(=\dfrac{\dfrac{2}{3}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}{\dfrac{5}{20}-\dfrac{5}{28}+\dfrac{5}{52}}\)

\(=\dfrac{\dfrac{2}{3}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}{\dfrac{5}{4}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}=\dfrac{2}{3}:\dfrac{5}{4}=\dfrac{2}{3}\cdot\dfrac{4}{5}=\dfrac{8}{15}\)

\(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)

\(=\dfrac{5}{22}-\dfrac{4}{22}+\dfrac{3}{13}-\dfrac{13}{8}+\dfrac{12}{8}\)

\(=\dfrac{1}{22}+\dfrac{3}{13}-\dfrac{1}{8}=\dfrac{173}{1144}\)

a: \(=\dfrac{1}{3}-\dfrac{37}{100}+\dfrac{1}{8}-\dfrac{32}{25}+\dfrac{-5}{2}+\dfrac{3}{2}\)

\(=\dfrac{1}{3}+\dfrac{1}{8}-1-\dfrac{37}{100}-\dfrac{128}{100}\)

\(=\dfrac{8+3-24}{24}-\dfrac{165}{100}\)

\(=\dfrac{-263}{120}\)

b: \(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)

\(=\dfrac{5}{22}-\dfrac{4}{22}-\dfrac{13}{8}+\dfrac{12}{8}+\dfrac{3}{13}\)

\(=\dfrac{1}{22}-\dfrac{1}{8}+\dfrac{3}{13}=\dfrac{173}{1144}\)

a: \(=\dfrac{1}{3}-\dfrac{37}{100}+\dfrac{1}{8}-\dfrac{32}{25}-\dfrac{5}{2}+\dfrac{3}{2}\)

\(=\dfrac{11}{24}+\left(-\dfrac{37}{100}+\dfrac{1}{8}-1\right)\)

\(=\dfrac{11}{24}-\dfrac{249}{200}=-\dfrac{59}{75}\)

b: \(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)

\(=\dfrac{5}{22}-\dfrac{4}{22}+\dfrac{3}{13}-\dfrac{13}{8}+\dfrac{12}{8}\)

\(=\dfrac{1}{22}+\dfrac{3}{13}-\dfrac{1}{8}=\dfrac{173}{1144}\)