#Java, 99 bytes

    void f(int a){int[]f=new int[2];while(++f[0]<=a){f[1]=f[0];while(f[1]>0)System.out.print(f[1]--);}}

EDIT 1: Saved few bytes by changing it from a full program to a function. 

Ungolfed:

    void f(int a) {
        int[] f = new int[2];
        while (++f[0] <= a) {
            f[1] = f[0];
            while (f[1] > 0) System.out.print(f[1]--);
        }
    }