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Find sum of the series 1-2+3-4+5-6+7....in C++
In this problem, we are given an integer value N. Our task is to find Sum of Series 1 - 2 + 3 - 4 + 5 - 6 + 7 upto n terms.
The series is 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10...
Let's take an example to understand the problem,
Input : N = 4 Output : -2
Explanation −
1 - 2 + 3 - 4 = -2
Solution Approach
A simple approach to solve the problem is finding the general term of the series and then finding the sum till n terms. And calculating the sum using formula will reduce the time to O(1).
The series is,
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10...
Let's find the sum of series for some values,
sum(1) = 1
sum(2) = 1 - 2 = -1
sum(3) = 1 - 2 + 3 = 2
sum(4) = 1 - 2 + 3 - 4 = -2
sum(5) = 1 - 2 + 3 - 4 + 5 = 3
sum(6) = 1 - 2 + 3 - 4 + 5 - 6 = -3
sum(7) = 1 - 2 + 3 - 4 + 5 - 6 + 7 = 4
sum(8) = 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 = -4
For here, we can conclude that the sum can be formulated as,
Sum = +(n+1)/2 if n is odd.
Sum = -(n)/2 if n is even.
Example
Program to illustrate the working of our solution
#include<iostream>
using namespace std;
int calcSumNTerms(int n) {
if(n%2 == 0)
return ((-1)*(n/2));
return ((n+1)/2);
}
int main() {
int n = 156;
cout<<"The sum of series upto n terms is "<<calcSumNTerms(n);
return 0;
}Output
The sum of series upto n terms is -78
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