Question

1+2+3+...+ n = 78 n=?

Answer 1

 

$\displaystyle\\1+2+3+...+n=78\\\\\text{Folosim formula lui Gauss.}\\\\\frac{n(n+1)}{2}=78\\\\n(n+1)=78\cdot2\\\\\text{Descompunem numarul 156.}\\\\156=2^2\times3\times13\\\\156=12\times13\\\\n(n+1)=12\times13\\\\n(n+1)=12(12+1)\\\\\implies \boxed{\bf n=12}\\\\\text{Verificare:}\\\\1+2+3+...+12=\frac{12(12+1)}{2}=6\times13=78~~~\text{Corect}$

Answer 2

Răspuns:

suma lui Gauss ;   S= (1+n) .n/2 78 ;  n(n+1)=78 .2;    n(n+1)=156 ;  n(n+1)=12 .13 ;  n=12

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