Question

se consideră mulțimea: A={4,7,10,13,16,.....,1993}. câte elemente are mulțimea? Calculați suma 4+7+10+...1993=

Answer 1

[tex]\text{Elementele sunt de forma 3k+1},k\in N^*.\\ 3k+1=1993\\ 3k=1992\\ k=664\Rightarrow card\ A=664\\ 4+7+10+_{\dots}+1993=\\ (3\cdot 1+1)+(3\cdot 2+1)+_{\dots}+(3\cdot 664+1)=\\ 3\cdot(1+2+3+_{\dots}+664)+664=\\ 3\cdot \frac{664\cdot 665}{2}+664=\\ 3\cdot 332\cdot 665+664=\\ 662340+664=\boxed{663004}[/tex]