Show life that you have a thousand reasons to smile
© Copyright 2024 DOKU.TIPS - All rights reserved.
Avem ca
1+5+9+...+(4*n+1)=
=(4*0+1)+(4*1+1)+(4*2+1)+...+(4*n+1)=
=4*(0+1+2+...+n)+1+1+...+1=
=4*(0+1+2+...+n)+(n+1)=
=(4*n*(n+1)/2)+(n+1)=2*n*(n+1)+(n+1)=
=(n+1)*(2*n+1)
Deci relatia din enunt este echivalenta cu
(n+1)(2*n+1)=231 care se reduce la o ecuatie de gradul 2 in necunoscuta n si are ca unica solutie naturala n=10 deci x=4*n+1=41