Sanask
a fost răspuns

se noteaza cu S indice A,suma elementelor multimii A={n/n=3k si k apartine M} si cu S indice B suma elementelor multimii B={n/n=4k si kapartine M},unde M={-1,-2,-3,....,-100}.

Calculati S indice A impartit la S indice B!

Răspuns :

[tex] \frac{ S_{A}}{ S_{B}} [/tex] = [tex] \frac{-3-6-9-...-300}{-4-8-12-...-400} [/tex] = [tex] \frac{3(-1-2-3-...-100)}{4(-1-2-3-...-100)} [/tex] = [tex] \frac{3}{4} [/tex]
A=(-3,-6,-9,.........-300)-precizez parantezele in acest caz sunt acolade 
B=(-4,-8,-12,.......-400)-idem ca mai sus
unde A-multimea A, B-multimea B
Sa=-3-6-9............-300=-3(1+2+3+.....100)
Sb=-4-8-12-.......400=-4(1+2+3+......100)
Sa/Sb=-3(1+2+3+......100)/-4(1+2+3+.....100)=-3/-4=3/4