Question

Determină suma multiplilor lui 2 cuprinsi intre 5 la puterea a 2 si 5 la puterea a 3

Answer 1

   
[tex]\displaystyle\\ 5^2 = 25\\ 25^2=125\\ \text{Multiplii lui 2 cuprinsi intre 25 si 125 sun numerele pare urmatoare:}\\ 26;~28;~30;~32; \cdots;~124\\ \text{Suma lor o calculam cu formula lui Gauss.}\\ \text{Numarul de termeni este: }\\\\ n = \frac{124-26}{2}+1 = \frac{98}{2}+1=49+1=\boxed{50~\text{de termeni}}\\\\ \text{Aplicam formula lui Gauss:}\\\\ 26+28+30+32+ \cdots +124= \frac{50(124+26)}{2}=25\times 150=\boxed{3750} [/tex]