Question

Inversul numărului 1/1×2+1/2×3+1/3×4 este

Answer 1

$N = \dfrac{1}{1\times2}+ \dfrac{1}{2\times3}+ \dfrac{1}{3\times4}\Big|\times (1\times 2\times 3\times 4) \\ \\ (1\times 2\times 3\times 4) \times N = \dfrac{1\times 2\times 3\times 4}{1\times 2}+\dfrac{1\times 2\times 3\times 4}{2\times 3}+\dfrac{1\times 2\times 3\times 4}{3\times 4} \\ \\ 24\times N = 3\times 4+1\times 4+1\times 2 \\ \\ 24\times N = 12+4+2 \\ \\ 24\times N = 18 \\ \\ N = \dfrac{18}{24 } \\ \\ N = \dfrac{3}{4} \\ \\ \dfrac{1}{N}=\dfrac{4}{3}$