Question

5+10+15+20+25+...+100 va rog cum se calculeaza?

Answer 1

5+10+15+20+25+...+100=
5×(1+2+3+4+5+....+20)=
1+2+3+...+20=
(1+20)×20:2=
420:2=210
5×210=1050

Answer 2

$\displaystyle 5+10+15+20+25+...+100= \\ \\ \texttt{Factor comun pe 5.} \\ \\ 5(1+2+3+4+5+...+20)= \\ \\ \texttt{Paranteza se rezolva cu formula:} \\ \\ \boxed{\frac{n(n+1)}{2} =} \\ \text{Unde n reprezinta ultimul nr din sir.} \\ \\ \frac{20(20+1)}{2}= \frac{\not20 \cdot 21}{\not2} =10 \cdot 21 =210 \\ \\ 5\cdot210=\underline{\bold{1050}}$