\(1+2+3+4+...+n=465\)
=> \(\frac{\left(n+1\right).n}{2}=465\)
=> \(\left(n+1\right).n=465.2\)
=> \(\left(n+1\right).n=930\)
=> \(\left(n+1\right).n=31.30\)
=> \(\left(n+1\right).n=\left(30+1\right).30\)
=> n = 30
=>(n+1).[(n-1)/1+1]/2=465
=>(n+1)n=930
=>(n+1)n=30.31
=>n=30