Question

(17+18+...146):5+(1345-174x3)

Answer 1

17+18+...+146=1+2+3+...+146-(1+2+3...+16)=(146·147)/2-(16·17)/2=21462/2-272/2=10731-136=10595

=> 10595:5+(1345-174·3)=2119+(1345-522)=2119+823=2942

Answer 2

$\displaystyle \mathtt{(17+18+...+146):5+(1345-174 \cdot 3)}\\ \\ 17+18+...+146\\ \\ 146=17+(n-1) \cdot 1 \Rightarrow 146=17+n-1 \Rightarrow n=130 \\ \\ \mathtt{S_{130}= \frac{2 \cdot 17+(130-1) \cdot 1}{2}\cdot 130 =(34+129) \cdot 65=163 \cdot 65=10595} \\ \\ \mathtt{(17+18+...+146):5+(1345-174 \cdot 3)=10595:5+(1345-522)=}\\ \\ \mathtt{=2119+823=2942} \\ \\ \mathbf{(17+18+...+146):5+(1345-174 \cdot 3)=2942}$