Question

Scrieti sub forma de fractie ordinara, ireductibila suma: S=1 /45 + 2/45+ 3/45 +.....+ 75/45
Unde,, / ,,este bara de fractie

Answer 1

$S = \frac{1}{45} + \frac{2}{45} + \frac{3}{45} + ... + \frac{75}{45}$

$S = \frac{1 + 2 + 3 + ... + 75}{45}$

$S = \frac{ \frac{75(75 + 1)}{2} }{45} = \frac{ \frac{75 \times 76}{2} }{45} = \frac{75 \times 38}{45} = \frac{5 \times 38}{3} = \frac{190}{3}$

Formulă :

$1+2+3+...+n=\frac{n(n+1)}{2}$