(Problem 6)Sum square difference
2013-07-26 11:02
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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.
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.
#include <stdio.h> #include <string.h> #include <ctype.h> #include <math.h> #define N 100 int powplus(int n, int k) { int s=1; while(k--) { s*=n; } return s; } int sum1(int n) { return powplus((n+1)*n/2,2); } int sum2(int n) { return (n*(n+1)*(2*n+1))/6; } void solve() { printf("%d\n",sum1(N)); printf("%d\n",sum2(N)); printf("%d\n",sum1(N)-sum2(N)); } int main() { solve(); return 0; }
Answer: | 25164150 |
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