The sum of the squares of the first ten natural numbers is,

1

² + 2

² + ... + 10

² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)

² = 55

² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025  385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

1 #include 
     
       2 #include 
      
        3 #include 
       
         4 #include 
        
          5    6 #define N 100 7    8 int powplus(int n, int k) 9 {10     int s=1;11     while(k--)12     {13        s*=n;14     }15   return s;16 }17   18 int sum1(int n)19 {20    return  powplus((n+1)*n/2,2);21 } 22   23 int sum2(int n)24 {25    return (n*(n+1)*(2*n+1))/6;26 }27   28 void solve()29 {30      printf("%d\n",sum1(N));31      printf("%d\n",sum2(N));32    printf("%d\n",sum1(N)-sum2(N));33 }34   35 int main()36 {37   solve();38   return 0;39 }
        
       
      
     

 

Answer:

25164150