\(1+2+...+n=465\)
\(\Rightarrow\frac{n\left(n+1\right)}{2}=465\)
\(\Rightarrow n\left(n+1\right)=930\)
\(\Rightarrow n\left(n+1\right)=30\cdot31\)
\(\Rightarrow n=30\)
1 + 2 + 3 + ... + n = 465
\(\Rightarrow\) n(1 + n) : 2 = 465
\(\Rightarrow\) n(1 + n) = 930
\(\Rightarrow\) n(1 + n) = 30 . (1 + 30)
\(\Rightarrow\) n = 30
\(\Rightarrow\)