Câu hỏi của Vũ Minh Khánh

Question

Tính nhanh 3/2×4+3/4×6+3/6×8+......+3/48×50 tính nhanh hộ mình với

Nguyễn Lê Phước Thịnh · Accepted Answer

$\dfrac{3}{2\text{x}4}+\dfrac{3}{4\text{x}6}+...+\dfrac{3}{48\text{x}50}$$=\dfrac{3}{2}\text{x}\left(\dfrac{2}{2\text{x}4}+\dfrac{2}{4\text{x}6}+...+\dfrac{2}{48\text{x}50}\right)$$=\dfrac{3}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)$$=\dfrac{3}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=\dfrac{3}{2}\text{x}\dfrac{24}{50}=\dfrac{36}{50}=\dfrac{18}{25}$Câu trả lời: $\dfrac{3}{2\text{x}4}+\dfrac{3}{4\text{x}6}+...+\dfrac{3}{48\text{x}50}$$=\dfrac{3}{2}\text{x}\left(\dfrac{2}{2\text{x}4}+\dfrac{2}{4\text{x}6}+...+\dfrac{2}{48\text{x}50}\right)$$=\dfrac{3}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)$$=\dfrac{3}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=\dfrac{3}{2}\text{x}\dfrac{24}{50}=\dfrac{36}{50}=\dfrac{18}{25}$

Pencil · Answer

$\dfrac{2}{3}A=\dfrac{2}{2\times4}+\dfrac{2}{4\times6}+...\dfrac{2}{48\times50}$

$\dfrac{2}{3}A=\dfrac{4-2}{2\times4}+\dfrac{6-4}{4\times6}+...+\dfrac{50-48}{48\times50}$

$\dfrac{2}{3}A=\dfrac{4}{2\times4}-\dfrac{2}{2\times4}+\dfrac{6}{4\times6}-\dfrac{4}{4\times6}+...+\dfrac{50}{48\times50}-\dfrac{48}{48\times50}$

$\dfrac{2}{3}A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}$

$\dfrac{2}{3}A=\dfrac{1}{2}-\dfrac{1}{50}$

$\dfrac{2}{3}A=\dfrac{12}{25}$

$A=\dfrac{12}{25}\div\dfrac{2}{3}$

$A=\dfrac{18}{25}$Câu trả lời: $\dfrac{2}{3}A=\dfrac{2}{2\times4}+\dfrac{2}{4\times6}+...\dfrac{2}{48\times50}$

$\dfrac{2}{3}A=\dfrac{4-2}{2\times4}+\dfrac{6-4}{4\times6}+...+\dfrac{50-48}{48\times50}$

$\dfrac{2}{3}A=\dfrac{4}{2\times4}-\dfrac{2}{2\times4}+\dfrac{6}{4\times6}-\dfrac{4}{4\times6}+...+\dfrac{50}{48\times50}-\dfrac{48}{48\times50}$

$\dfrac{2}{3}A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}$

$\dfrac{2}{3}A=\dfrac{1}{2}-\dfrac{1}{50}$

$\dfrac{2}{3}A=\dfrac{12}{25}$

$A=\dfrac{12}{25}\div\dfrac{2}{3}$

$A=\dfrac{18}{25}$

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