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\(K=\left(1-\dfrac{3}{2\cdot4}\right)\left(1-\dfrac{3}{3\cdot5}\right)\cdot...\cdot\left(1-\dfrac{3}{19\cdot21}\right)\)
\(=\dfrac{3^2-1-3}{\left(3-1\right)\left(3+1\right)}\cdot\dfrac{4^2-1-3}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{20^2-4}{\left(20-1\right)\left(20+1\right)}\)
\(=\dfrac{\left(3-2\right)\left(3+2\right)}{\left(3-1\right)\left(3+1\right)}\cdot\dfrac{\left(4-2\right)\left(4+2\right)}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{18\cdot22}{\left(20-1\right)\left(20+1\right)}\)
\(=\dfrac{1\cdot5}{2\cdot4}\cdot\dfrac{2\cdot6}{3\cdot5}\cdot...\cdot\dfrac{18\cdot22}{19\cdot21}\)
\(=\dfrac{1\cdot2\cdot3\cdot...\cdot21\cdot22}{2\cdot3\cdot4\cdot5\cdot...\cdot19\cdot20\cdot21}=1\cdot22=22\)
bạn ơi , đây là cộng trừ các số lẻ đúng ko ?
nếu vậy thì tại sao lại có số 14 ở đây ?
SSH: (399-1):2+1= 200
Neu chia moi nhom 4 so thi so cap so la:
200:4 = 50
Ta co:
B=1+3-5-7+9+11-13-15+...+393+395-397-399
B= (1+3-5-7)+(9+11-13-15)+...+(393+395-397-399)
B= -8 + -8 +...+ -8
B= -8 . 50
B= -400
SSH: (399-1):2+1= 200
Neu chia moi nhom 4 so thi so cap so la:
200:4 = 50
Ta co:
A=1+3-5-7+9+11-13-15+...+393+395-397-399
A= (1+3-5-7)+(9+11-13-15)+...+(393+395-397-399)
A= -8 + -8 +...+ -8
A= -8 . 50
A= -400
a.
\(\left(1\frac{1}{4}+\frac{3}{5}\right):\left(-\frac{11}{12}\right)+\left(\frac{3}{8}-1\frac{2}{5}\right):\left(-\frac{11}{12}\right)\)
\(=\left(\frac{5}{4}+\frac{3}{5}+\frac{3}{8}-\frac{7}{5}\right):\left(-\frac{11}{12}\right)\)
\(=\left(\frac{13}{8}-\frac{4}{5}\right):\left(-\frac{11}{12}\right)\)
\(=\frac{33}{40}:\left(-\frac{11}{12}\right)\)
\(=\frac{33}{40}\cdot\left(-\frac{12}{11}\right)\)
\(=\frac{-9}{10}\)
b.
\(\left(\frac{3}{8}-1\frac{2}{5}\right):\left(-\frac{11}{15}\right)+\left(1\frac{1}{4}+\frac{3}{5}\right):\left(-\frac{11}{15}\right)\)
\(=\left(\frac{3}{8}-\frac{7}{5}+\frac{5}{4}+\frac{3}{5}\right):\left(-\frac{11}{15}\right)\)
\(=\left(\frac{13}{8}-\frac{4}{5}\right):\left(-\frac{11}{15}\right)\)
\(=\frac{33}{40}:\left(-\frac{11}{15}\right)\)
\(=\frac{33}{40}\cdot\left(-\frac{15}{11}\right)\)
\(=\frac{-9}{8}\)
a) \(-\frac{4}{15}\cdot\left(-\frac{3}{8}\right)\cdot\left(\frac{15}{-4}\right)\cdot8\)
\(=\left(-\frac{4}{15}\cdot\left(\frac{15}{-4}\right)\right)\cdot\left(-\frac{3}{8}\cdot8\right)\)
\(=1\cdot\left(-3\right)=-3\)
b) \(-\frac{2}{3}\cdot\frac{4}{19}+\frac{5}{3}\cdot\frac{4}{19}\)
\(=\frac{4}{19}\cdot\left(\frac{5}{3}-\frac{2}{3}\right)\)
\(=\frac{4}{19}\cdot1=\frac{4}{19}\)
c) \(-\frac{1}{2}\cdot\frac{5 }{3}+\frac{1}{2}\cdot\frac{8}{3}\)
\(=\frac{1}{2}\left(\frac{8}{3}-\frac{5}{3}\right)\)
\(=\frac{1}{2}\cdot1=\frac{1}{2}\)
