Question

5/125 - 10/125 + 15/125 - 20/125 +...+115/125-120/125 =


FASTT dau coroana

Answer 1

$\dfrac{5}{125}-\dfrac{10}{125}+\dfrac{15}{125}-\dfrac{20}{125}+...+\dfrac{115}{125}-\dfrac{120}{125}= \\ \\ =\dfrac{5}{125}\cdot(1-2+3-4+...+23-24) = \\ \\ = \dfrac{5}{125}\cdot(-1-1-1-\underset{\text{de 12 ori}}{........}-1) = \\ \\ = \dfrac{5}{125}\cdot (-12) = \\ \\ =\dfrac{1}{25}\cdot(-12) = \\ \\ = -\dfrac{12}{25}$