\(1\dfrac{1}{3}.1\dfrac{1}{8}.1\dfrac{1}{15}.....1\dfrac{1}{99}\)

\(=\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{100}{99}\)

\(=\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{10.10}{9.11}\)

\(=\dfrac{2.3.4.....10}{1.2.3.....9}.\dfrac{2.3.4.....10}{3.4.5.....11}\)

\(=10.\dfrac{2}{11}\)

\(=\dfrac{20}{11}\)

\(C=\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{399}\)

\(C=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{19.21}\)

\(C=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{19}-\dfrac{1}{21}\)

\(C=\dfrac{1}{3}-\dfrac{1}{21}\)

\(C=\dfrac{2}{7}\)

sư tử chặn đường sao mài đi

Tập hợp con của M có một phần tử trở lên là:

\(\left\{1\right\};\left\{2\right\};\left\{3\right\};\left\{4\right\}\)

\(\left\{1,2\right\};\left\{1,3\right\};\left\{1,4\right\};\left\{2,3\right\};\left\{2,4\right\};\left\{3;4\right\}\)

\(\left\{1,2,3\right\};\left\{1,2,4\right\};\left\{1,3,4\right\};\left\{2;3;4\right\}\)

\(\left\{1,2,3,4\right\}\)

Vậy có tất cả 15 tập hợp.

còn lại bạn tự tính nhé

\(\dfrac{1}{5.8}+\dfrac{1}{8.11}+\dfrac{1}{11.14}+...+\dfrac{1}{x.\left(x+3\right)}=\dfrac{101}{1540}\)

\(\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)=\dfrac{101}{1540}\)

\(\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{x-3}\right)=\dfrac{101}{1540}\)

\(\dfrac{1}{5}-\dfrac{1}{x-3}=\dfrac{101}{1540}:\dfrac{1}{3}\)