+526 If \({△}_{k}=\begin{vmatrix} 2.3^{k-1} && 3.4^{k-1} && 4.5^{k-1} \\ \alpha && \beta && \gamma \\ 3^n-1 && 4^n-1 && 5^n-1 \end{vmatrix}\\ \) then the value of \(\sum_{n}^{k=1}{△}_{k} \) depends
1) only on \(\alpha, \beta\) and not on \(\gamma\)
2) on none of \(\alpha, \beta\) and \(\gamma\)
3) on all of \(\alpha, \beta \) and \(\gamma\)
4) only on \(\alpha \) not on \(\beta\) and \(\gamma\)
Also give possible explanation for the same. \(\)
