Question

Calculati:

1+3+5+7+ .........+ 199

Answer 1

$\displaystyle 1+3+5+7+...+199= \\ \\ =1+2+3+4+5+6+7+...+199-(2+4+6+...+198)= \\ \\ = \frac{199(199+1)}{2} -2 (1+2+3+...+99)= \\ \\ = \frac{199 \times 200}{2} -2 \times \frac{99(99+1)}{2} = \frac{39800}{2} -2 \times \frac{99 \times 100}{2} = \\ \\ =19900-\not2 \times \frac{9900}{\not2} =19900-9900=10000$