math - Solving Recurrences in Loops -

i understand how solve recurrence relations when not involve additional looping i.e.:

int recursive_method(int n){     if(n == 1){        return 1;     }     constant statement;     recursive_method(n-1);      return n; } 

my problem comes when trying solve recurrences inside of loops following:

int recursive_method(int n){         if(n == 1){            return 1;         }         for(int = 1; i<n; i++){            constant statement;            recursive_method(n-1);         }         return n; } 

when trying set recursive relation problem above

t(n) = 1 if n<2;         sum(from i=1 n){t(n-1) + c} if n>=2 

so in other words sum of costs 1 n? if not, how go thinking problem this?

the expression have t(n) in recursive case right, can simplified. in particular, notice work done in sum independent of summation index, can rewrite

sum i=1 n { t(n-1) + c }

as

nt(n - 1) + cn

so you'll end with

t(n) = 1 (if n ≤ 1)

t(n) = nt(n - 1) + cn (otherwise)