Question

\(\left(\frac{1}{2}-1\right):\left(\frac{1}{3}-1\right):\left(\frac{1}{4}-1\right):...:\left(\frac{1}{99}-1\right):\left(\frac{1}{100}-1\right)\)

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Ai nhanh mik tick!!!!!!!!!!!!

 

 

 

Answer 1

\(\left(\frac{1}{2}-1\right):\left(\frac{1}{3}-1\right):\left(\frac{1}{4}-1\right):...:\left(\frac{1}{100}-1\right)\)

\(=\frac{-1}{2}:\frac{-2}{3}:\frac{-3}{4}:...:\frac{-98}{99}:\frac{-99}{100}\)

\(=\frac{-1\cdot3\cdot4\cdot...\cdot99\cdot100}{2\cdot\left(-2\right)\cdot\left(-3\right)\cdot...\cdot\left(-98\right)\cdot\left(-99\right)}\)

\(=\frac{\left(-1\right)^{99}\cdot100}{2\cdot\left(-2\right)}=\frac{-1\cdot100}{-4}=\frac{-100}{4}=-25\)

- P/s: Không chắc chắn nhé!