The sum of the squares of the first ten natural numbers is,
12 + 22 + ... + 102 = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)2 = 552 = 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 <stdio.h> 2 #include <string.h> 3 #include <ctype.h> 4 #include <math.h> 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:
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25164150 |