Observam ca la fiecare suma termenii sunt in progresie aritmetica.
In acest caz suma lor o calculam folosind formula lui Gauss.
[tex]\displaystyle\\
S_1=2+4+6+ \cdots + 100\\
\text{Calculam numarul de termeni:}\\\\
n = \frac{100-2}{2}+1 =\frac{98}{2}+1 =49+1=50~\text{ de termeni}\\\\
S_1=2+4+6+ \cdots + 100= \frac{50(100+2)}{2} = 25\times 102=\boxed{2550} [/tex]
[tex]\displaystyle\\
S_2=3+5+7+ \cdots + 101\\
\text{Calculam numarul de termeni:}\\\\
n = \frac{101-3}{2}+1 =\frac{98}{2}+1 =49+1=50~\text{ de termeni}\\\\
S_2=3+5+7+ \cdots + 101= \frac{50(101+3)}{2} = 25\times 104=\boxed{2600} [/tex]
[tex]\displaystyle\\
S_3=4+6+8+ \cdots + 102\\
\text{Calculam numarul de termeni:}\\\\
n = \frac{102-4}{2}+1 =\frac{98}{2}+1 =49+1=50~\text{ de termeni}\\\\
S_3=4+6+8+ \cdots + 102= \frac{50(102+4)}{2} = 25\times 106=\boxed{2650}[/tex]
