Question

calculați 43+45+47+...+97

Answer 1

$\displaystyle 43+45+47+...+97 \\ \\ 97=43+(n-1) \cdot 2 \Rightarrow 97=43+2n-2 \Rightarrow 2n=56 \Rightarrow n= \frac{56}{2} \Rightarrow \\ \\ \Rightarrow n=28 \\ \\ S_{28}= \frac{2 \cdot 43+(28-1) \cdot 2}{2} \cdot 28 \\ \\ S_{28}=(86+27 \cdot 2) \cdot 14 \\ \\ S_{28}=(86+54) \cdot 14 \\ \\ S_{28}=140 \cdot 14 \\ \\ S_{28}=1960 \\ \\ 43+45+47+...+97=1960$