Răspuns :
[tex]\displaystyle \\ 4+6+8+ \cdots +30 -1-3-5- \cdots -37 = ~? \\ \\ \text{Sirul este format din doua subsiruri, } S_1 ~si~S_2 \\ \\ \text{Calculam suma sirului }S_1. \\ \\ S_1 = 4+6+8+ \cdots +30 \\ \text{Calculam numarul de termeni:} \\ \\ n_1 = \frac{30-4}{2}+1 = \frac{26}{2}+1 =13+1=\boxed{14~termeni} \\ \\ S_1 = \frac{14(30+4)}{2}=7\times 34 =\boxed{238} \\ \\ --- [/tex]
[tex]\displaystyle \\ \text{Calculam suma sirului }S_2. \\ \\ S_2 = -1-3-5- \cdots -37 = - ( 1+3+5+ \cdots +37) \\ \text{Calculam numarul de termeni:} \\ \\ n_2 = \frac{37-1}{2}+1 = \frac{36}{2}+1 =18+1=\boxed{19~termeni} \\ \\ S_2 = -\frac{19(37+1)}{2}= -\frac{19(38)}{2}= -19\times 19 =\boxed{-361} \\ \\ S = S_1+S_2 = 238 + (-361) = 238-361 = \boxed{\boxed{-123}} [/tex]
