Question

daca 2+4+6+...+abc=abc00,atunci abc apartine {.............} PLS ÎMI TREBUIE REPEDE

Answer 1

2=2*1
4=2*2
6=2*3
.........
abc=2*n
2+4+6+....+abc=2(1+2+3+...+n)=2n(n+1):2=n(n+1)
abc000=abc*100=2n*100=200n
n(n+1)=200n
n^2+n-200n=0
n^2-199n=0
n(n-199)=0
Deoarece produsul a doi factori e 0 cel putin unul dintre termeni este 0
n1=0
n2=199
Pentru:
n=0
abc=0⇒nu e numar de 3 cifre deci nu convine
n=199
abc=398⇒convine
Proba:
2+4+6+....+398
2n=398
n=199
2+4+6+...+398=199*200=39800
abc00=398*100=39800