Question

Rezolvati suma:1+3+5+...+201=?

Answer 1

$\displaystyle 1+3+5+...+201 \\ \\ 201=1+(n-1) \times 2 \\ \\ 201=1+2n-2 \\ \\ 2n=201-1+2 \\ \\ 2n=202 \\ \\ n= \frac{202}{2} \\ \\ n=101$

$\displaystyle S_{101}= \frac{2+100 \times 2}{2} \times 101 \\ \\ S_{101}= \frac{2+200}{2} \times 101 \\ \\ S_{101}= \frac{202}{2} \times 101 \\ \\ S_{101}=101 \times 101 \\ \\ S_{101}=10201$