Question

suma GAUSS,ajutor,5+10+15+.....+2010.
Va rog ajutati-ma ,dau coroana,nu stiu, va rog ajutati-ma,cine ma ajuta,sunteti cei mai tari.
Va rog!!!

Answer 1

aflam numarul de termeni
[(2010-5):5]+1=(2005:5)+1=401+1=402

S=5+10+15+.....+2010=[402(2010+5)]/2=(402*2015)/2=810030:2=405015

Answer 2

$\displaystyle \boxed{ \frac{n(n+1)}{2} } \\ \\\text{Suma lui Gaus: n e ultimul numar din sir, se aplica la sirul 1+2+3+...} \\ \\ \\ 5+10+15+.....+2010= \\ \text{Se da 5 factor comun, adica pui 5 in fata si ce ramane e impartit la 5} \\ \\ 5(1+2+3+...+402)= \\\\ \frac{n(n+1)}{2} = \frac{402(402+1)}{2} = \frac{402 \cdot403}{2} = 201 \cdot 403 = 81.003 \\ \\ 5\cdot81.003=\boxed{\boxed{405.015}}$