Question

Calculează: 1,1+2,2+3,3+...+9,9. Dau coroana!!

Answer 1

$1.1 + 2.2 + 3.3 + ... + 9.9 = \\ \\ \dfrac{11}{10} + \dfrac{22}{10} + \dfrac{33}{10} + ... + \dfrac{99}{10} = \\ \\ \\ \frac{11 + 22 + 33 + ... + 99}{10} = \\ \\ \\ \dfrac{11 \cdot(1 + 2 + 3 + ... + 9)}{10} = \\ \\ \\ \dfrac{11 \cdot(9 \cdot10 \div 2)}{10} = \\ \\ \\ \dfrac{11 \cdot(90 \div 2)}{ 10} = \\ \\ \\ \dfrac{11 \cdot45}{10} = \dfrac{495}{10} = 49.5$