Question

calculați (22+44+...+2024):(11+22+...+1012

Answer 1

(22 + 44 + ... + 2024) : (11 + 22 + ... + 1012) =

= 2·(11 + 22 + ... + 1012) : (11 + 22 + ... + 1012)

= 2

Answer 2

2 progresii aritmetice, prima cu ratia r =22, a1=22, an=2024, pentru a afla suma Sn aflam nr termenilor, an=a1+(n-1)r, 2024=22+(n-1)22, 2024=22+22n-22,

n=2024/22=92, Sn=n(a1+a92)/2=92(22+2024)/2=(92x2046)/2=188232/2=94116

a doua progresie aritmetica, r=11, a1=11, an=1012, 1012=11+(n-1)x11, 1012=11+11n-11

n=1012/11=92, Sn=92(11+1012)/2=(92x1023)/2=94116/2=47058

rezultatul impartirii=94116/47058=2