Breaking fractions

Algebra Level 2

The following two equations are true: 1 1 − 1 2 = 1 1 × 2 1 1 − 1 2 − 1 3 = 1 1 × 2 × 3 . \begin{array} { r c l } \dfrac 11 - \dfrac12& =& \dfrac1{1\times2} \\ \dfrac 11 - \dfrac12 -\dfrac13 &=& \dfrac1{1\times2\times 3}. \end{array} Is it also true that 1 1 − 1 2 − 1 3 − 1 4 = 1 1 × 2 × 3 × 4 ? \dfrac 11 - \dfrac12 -\dfrac13 - \dfrac14 = \dfrac1{1\times2\times 3\times4} ?

No, it is not true Yes, it is true

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Steven Jim
Apr 13, 2017

1/2 + 1/3 + 1/4 > 1 so LHS < 0. But RHS > 0 so this can't be true.

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Munem Shahriar
Jan 26, 2018

1 1 − 1 2 − 1 3 − 1 4 \dfrac 11 - \dfrac12 -\dfrac13 - \dfrac14

= 1 × 12 − 1 × 6 − 1 × 4 − 1 × 3 12 = \dfrac{1 \times 12 - 1 \times 6 - 1 \times 4-1 \times 3}{12}

= − 1 12 = -\dfrac 1{12}

Hence false.

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