Question

Calculați suma 1+3+5+........+99

Answer 1

1+2+3+...+99-2-4-6-...-98=
[tex]\frac{99*100}{2}-2(1+2+3+...+49)=\\ 99*50-\not 2*\frac{49*50}{\not2}=\\ 50(99-49)=50^2=2500[/tex]

Answer 2

$\displaystyle 1+3+5+...+99 \\ \\ 99=1+(n-1) \times 2 \\ \\ 99=1+2n-2 \\ \\ 2n=99-1+2 \\ \\ 2n=100 \\ \\ n= \frac{100}{2} \\ \\ n=50$

$\displaystyle S_{50}= \frac{2+49 \times 2}{2} \times 50 \\ \\ S_{50}= \frac{2+98}{2} \times 50 \\ \\ S_{50}= \frac{100}{2} \times 50 \\ \\ S_{50}=50 \times 50 \\ \\ S_{50}=2500$