$[40$pts$]$

Given these two methods: METHOD math$1$: public int math$1($ int n $)\{$ if $($n $<=1)\{$ return $1$; $\}//$ if else $\{$ return $($ n $*2)+$ math$1($ n$-1)$; $\}//$ else $\}//$ math$1$ METHOD math$2$: public int math$2($ int n $)\{$ if $($n $<=1)\{$ return $1$; $\}//$ if else $\{$ return n $+$ math$1($ n $)*$ math$2($ n$/2)$; $\}//$ else $\}//$ math$2($a$)$ Set up a recurrence relation for the running time of the method math$1$ as a function of n$.$ Solve your recurrence relation to specify THETA bound of math$1.($b$)$ Now set up a recurrence relation for the running time of the method math$2$ as a function of n$.$ Solve your recurrence relation to specify the Big$-$O bound of math$2.$ HINT: When doing this, the call to math$1$ can be replaced by the equation that you found when solving the recurrence relation for math$1$ in part $($a$)).$