Compute sum of digits in all numbers from 1 to n

In this problem, we have to find the sum of digits of all numbers in range 1 to n. For an example the sum of digits of 54 is 5 + 4 = 9, Like this, we have to find all the numbers and their sum of digits.

We know that there are 10^{d - 1} numbers can be generated, whose number of digits is d. To find the sum of all those numbers of digit d, we can use a recursive formula.

sum(10^d- 1)=sum(10^d-1- 1)*10+45*(10^d-1)

Input and Output

Input:
This algorithm takes the upper limit of the range, say it is 20.
Output:
Sum of digits in all numbers from 1 to n. Here the result is 102

Algorithm

digitSumInRange(n)

Input: The upper limit of the range.

Output − the sum of digits for all number in the range (1-n).

Begin
   if n 
Example
#include
#include
using namespace std;

int digitSumInRange(int n) {
   if (n> n;
   cout 
Output
Enter upper limit of the range: 20
Sum of digits in range (1 to 20) is: 102