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a) \(M=\frac{2\times2}{1\times5}+\frac{2\times2}{5\times9}+\frac{2\times2}{9\times13}+...+\frac{2\times2}{45\times40}\)
\(M=\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+...+\frac{4}{45\times49}\)
\(M=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{45}-\frac{1}{49}\)
\(M=1-\frac{1}{49}\)
\(M=\frac{48}{49}\)
b) \(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+5+...+10}\)
= \(\frac{2}{2\times\left(1+2\right)}+\frac{2}{2\times\left(1+2+3\right)}+...+\frac{2}{2\times\left(1+2+3+...+10\right)}\)
\(=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{110}\)
\(=\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{10\times11}\)
\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(=2\times\frac{9}{22}\)
\(=\frac{9}{11}\)
Mình trả lời câu a nha M= 4/1*5+4/5*9+4/9*13+...+4/45*49 M=1-1/5+1/5-1/9+1/9-1/13+...+1/45-1/49 M=1-1/49=48/49
\(50\%+\dfrac{1}{2}+\dfrac{1}{7}\times\dfrac{2}{5}+\dfrac{1}{7}\times\dfrac{3}{5}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{2}{35}+\dfrac{3}{35}\)
\(=1+\dfrac{5}{35}\)
\(=1+\dfrac{1}{7}\)
\(=\dfrac{8}{7}\)
\(50\%+\dfrac{1}{2}+\dfrac{1}{7}x\dfrac{2}{5}+\dfrac{1}{7}x\dfrac{3}{5}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{7}x\left(\dfrac{2}{5}+\dfrac{3}{5}\right)\)
\(=1+\dfrac{1}{7}x1\)
\(=\dfrac{7}{7}+\dfrac{1}{7}=\dfrac{8}{7}\)
50% + 1/2 + 1/7 × 2/5 + 1/7 × 3/5
= 1/2 + 1/2 + 1/7 × (2/5 + 3/5)
= 1 + 1/7 × 1
= 1 + 1/7
= 7/7 + 1/7
= 8/7
2,016 x 20,17 x 201,8 x (1/4 + 2/5 - 13/26)
= 2,016 x 20,17 x 201,8 x 0,15
= 40,66272 x 201,8 x 0,115
= 8205,736896 x 0,15
= 1230,860534
Bạn cứ tình máy tình là ra. Kết bạn với mình nha!
=\(\dfrac{4}{3}+\dfrac{9}{8}+\dfrac{16}{15}+...+\dfrac{100}{99}\)
=\(\frac{2.2}{1.3}\)+\(\frac{3.3}{2.4}\)+.....+\(\frac{10.10}{9.11}\)
=\(\frac{2.3......10}{1.2.3.....9}\)+\(\frac{2.3.4....10}{3.4.5......11}\)
=\(10+\dfrac{2}{11}\)
=\(10\frac{2}{11}\)
\(=1\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=1\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
cậu thử hỏi người đưa ra câu hỏi xem hai chúng mk ai sai ai đúng
\(A=\left(1\frac{1}{7}\right).\left(1\frac{1}{8}\right).\left(1\frac{1}{9}\right)...\left(1\frac{1}{50}\right)\)
\(A=\frac{8}{7}.\frac{9}{8}.\frac{10}{9}...\frac{51}{50}\)
\(A=\frac{8.9.10...51}{7.8.9...50}\)
\(\Rightarrow A=\frac{51}{7}\)