Question

28+29+30+......+2000=


va rog sa ma ajutati

Answer 1

$\displaystyle 28+29+30+...+2000 \\ \\ 2000=28+(n-1) \cdot 1 \Rightarrow 2000=28+n-1 \Rightarrow n=1973 \\ \\ S_{1973}= \frac{2 \cdot 28+(1973-1) \cdot 1}{2} \cdot 1973 \\ \\ S_{1973}= \frac{56+1972 \cdot 1}{2} \cdot 1973 \\ \\ S_{1973}= \frac{56+1972}{2} \cdot 1973 \\ \\ S_{1973}= \frac{2028}{2} \cdot 1973 \\ \\ S_{1973}=1014 \cdot 1973 \\ \\ S_{1973}=2000622$