Question

Cum se rezolva:1+3+5+7+...+199? Va rog ajutati-ma!!!

Answer 1

Se numeste o suma de tip Gauss.
199x(199+1):2=
=199x200:2=
=199x100=19.900

Answer 2

$\displaystyle 1+3+5+7+...+199 \\ \\ 199=1+(n-1) \times 2 \\ \\ 199=1+2n-2 \\ \\ 2n=199-1+2 \\ \\ 2n=200 \\ \\ n= \frac{200}{2} \\ \\ n=100$

$\displaystyle S_{100}= \frac{2+99 \times 2}{2} \times 100 \\ \\ S_{100}= \frac{2+198}{2} \times 100 \\ \\ S_{100}= \frac{200}{2} \times 100 \\ \\ S_{100}=100 \times 100 \\ \\ S_{100}=10000$