Question

1+3+5+…+99= Suma lui Gauss

Answer 1

suma de 50 numere impare 
suma = ( 1 + 99 ) · 50 / 2 
= 100 · 50 :2 
= 100 · 25 
 = 2500 

Answer 2

$\displaystyle 1+3+5+...+99= \\ \\ =1+2+3+4+5+...+99-(2+4+6+...+98)= \\ \\ = \frac{99(99+1)}{2} -2(1+2+3+...+49)= \frac{99 \times 100}{2} -2 \times \frac{49(49+1)}{2} = \\ \\ = \frac{9900}{2} -2 \times \frac{49 \times 50}{2} =4950-\not2 \times \frac{2450}{\not2} =4950-2450=2500$