Use the substitution method to show that for the recurrence equation: T( 1 )=8 T( n )=T(n-1) + 4n the solution is T( n )= ( n2 ).

Use the substitution method to show that for the recurrence equation: T( 1 )=1 T( n )=T( n/2 ) + n the solution is T( n )=O ( n ).

Use the recursion tree method to find an asymptotic upper bound for the recurrence equation: T( n )=T( n/2) + n2 Use substitution method to prove your answer.