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Here we will see if one number can be represented as sum of two or more consecutive numbers or not. Suppose a number is 12. This can be represented as 3+4+5.

There is a direct and easiest method to solve this problem. If a number is power of 2, then it cannot be expressed as sum of some consecutive numbers. There are two facts that we have to keep in mind.

- Sum of any two consecutive numbers is odd, then one of them will be odd, another one is even.
- Second fact is 2
^{n}= 2^{(n-1)}+ 2^{(n-1)}.

#include <iostream> using namespace std; bool isSumofconsecutiveNumbers(int n) { if((n & (n-1)) && n){ return true; } else { return false; } } int main() { int num = 36; if(isSumofconsecutiveNumbers(num)){ cout << "Can be represented"; } else { cout << "Cannot be represented"; } }

Can be represented

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