$2.(20$ points$)$ Give the tightest big$-$O expression in terms of $\backslash ($ n $\backslash )$ to describe the time complexity of each program below, if it terminates; otherwise, write $\backslash (\backslash$infty $\backslash ).$

a$)$ while $\backslash ($ n$>1\backslash )$

b$)$ while $\backslash (\backslash$mathrm$\{$n$\}$

eq $1\backslash )$