Question

S = 11 + 13 + 15 +...+103

si

S = 15 + 19 + 23 +...+ 159

Aflati cu Suma lui Gauss​

Answer 1

 

$\displaystyle\bf\\ 1)\\S=11+13+15+...+103\\\\Calculam~numarul~de~termeni:\\\\n=\frac{103-11}{2}+1=\frac{92}{2}+1=46+1=47~de~termeni\\\\Calculam~suma~cu~Gauss: \\\\S=\frac{n(103+11)}{2}=\frac{47(103+11)}{2}=\frac{47\times114)}{2}=47\times57=\boxed{\bf2679}$

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$\displaystyle\bf\\2)\\S=15+19+23+...+159\\\\Calculam~numarul~de~termeni:\\\\n=\frac{159-15}{4}+1=\frac{144}{4}+1=36+1=37~de~termeni\\\\Calculam~suma~cu~Gauss:\\\\S=\frac{n(159+15)}{2}=\frac{37(159+15)}{2}=\frac{37\times174)}{2}=37\times87=\boxed{\bf3219}$