Question

Calculati: 1+3+5+...+19

Answer 1

$\displaystyle 1+3+5+...+19 \\ \\ 19=1+(n-1) \times 2 \\ \\ 19=1+2n-2 \\ \\ 2n=19-1+2 \\ \\ 2n=20 \\ \\ n= \frac{20}{2} \\ \\ n=10$

$\displaystyle S_{10}= \frac{2+9 \times 2}{2} \times 10 \\ \\ S_{10}= \frac{2+18}{2} \times 10 \\ \\ S_{10}= \frac{20}{2} \times 10 \\ \\ S_{10}=10 \times 10 \\ \\ S_{10}=100$