Question

Aflati nr natural n stiind ca :
1 supra 6+1 supra 12+1 supra 20+...+1 supra n·(n+1)=999 supra 2000

COROANA!

Answer 1

1/2 - 1/3   +  1/3-1/4   +  1/4-1/5   +...+1/n - 1/(n+1) = 1/2 - 1/(n+1) = (n+1-2)/2(n+1) = (n-1)/2(n+1) = 999/2*1000 ⇒ (n-1)/(n+1)=999/1000 nu are solutie in N.

Daca ar fi fost 998 in loc de 999 in enunt, at n=999.