If we take a look at this problem carefully, we can see that the idea of “loop” is to track some counter value e.g. “i=0” till “i <= 100”. So if we aren’t allowed to use loop, how else can be track something in C language! 
Well, one possibility is the use of ‘recursion’ provided we use the terminating condition carefully. Here is a solution that prints numbers using recursion. 

Method-1:

#include 

// Prints numbers from 1 to n
void printNos(unsigned int n)
{
	if(n > 0)
	{
		printNos(n - 1);
		printf("%d ", n);
	}
	return;
}

// Driver code
int main()
{
	printNos(100);
	getchar();
	return 0;
}

Output : 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 
16 17 18 19 20 21 22 23 24 25 26 27 
28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50 51
52 53 54 55 56 57 58 59 60 61 62 63
64 65 66 67 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 84 85 86 87
88 89 90 91 92 93 94 95 96 97 98 99 
100

Method 2:

C++

// C++ program
#include <bits/stdc++.h>
using namespace std;

void printNos(int initial, int last)
{
	if (initial <= last) {
		cout << initial << " ";
		printNos(initial + 1, last);
	}
}

int main()
{
	printNos(1, 100);
	return 0;
}

// This code is contributed by ukasp.

Output

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100