Răspuns :
[tex]\displaystyle\bf\\Calculati: \\\\11+12+13+...+52\\\\Rezolvare:\\\\Pasul~1: Calculam~numarul~de~termeni~(n).\\\\n=52-11+1=41+1=42~de~termeni\\\\Pasul~2:Aplicam~formula~lui~Gauss.\\\\S=\frac{n(52+11)}{2}=\frac{42\times63}{2}=21\times63=\boxed{\bf1323}[/tex]
11+12+13+...+52
=(1+2+3+...+52)-(1+2+...+10)
=[52*(52+1)]/2-[10*(10+1)]/2
=(52*53)/2-(10*11)/2
=26*53-5*11
=1378-55
=1323
suma lui Gauss: [n(n+1)]/2
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