Question

Calculați 1/(2•3)+1/(3•4)+1/(4•5)-3/10

Answer 1

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Answer 2

$\it \dfrac{1}{2\cdot3} = \dfrac{1}{2}- \dfrac{1}{3} \\ \\ \\ \dfrac{1}{3\cdot4} = \dfrac{1}{3} - \dfrac{1}{4} \\ \\ \\ \dfrac{1}{4\cdot5} = \dfrac{1}{4}- \dfrac{1}{5}$

După reduceri, suma algebrică din enunț devine:

$\it \dfrac{^{5)}1}{\ 2} - \dfrac{^{2)}1}{\ 5}- \dfrac{3}{10} = \dfrac{5-2-3}{10} = \dfrac{0}{10} = 0$