CODEWITHSUNDEEP
c++
jack23
jack23

Reputation: 21

Sum a sequence of positive and negative fraction

I have a homework to make an algorithms for sum this sequence : S = 1 - 1/2 + 1/4 - 1/6 + 1/8 - 1/10 + ... + 1/2n if the user input 2 the sum will be 1 - 1/2 = 1/2 and etc.

Here is my coding :

int main() {

    int num, N, k;
    double S;
    cout << "enter the sequence : ";
    cin >> N;
    for (num = 1, k = 0, S = 1; num <=N; num++) {
        num++;
        k=+2;
        if (num % 2 == 0) {
            S -= 1/k;
        } else {
            S += 1/k;
        }
    }
    cout << "The sum is " << S;
    system("PAUSE");
    return 0;
}

I'm so confused why the sum always refer to 1 ?? Can anyone explain to me why this happen??

Upvotes: 2

Views: 1122

Answers (3)

user1726343
user1726343

Reputation: 

for(num = 1, sum = 1; num <=N; num++){
    if(num%2==0){
        sum += 1/(num*2);
    }else{
        sum -= 1/(num*2);
    }
}

That should do it, provided the nth term in your sequence is (1/((n-1)*2)).

EDIT: As pointed out below, when performing division, one of the operands needs to be non integer to prevent the result from being an integer. The correction to my attempt above would be:

for(num = 1, sum = 1; num <=N; num++){
    if(num%2==0){
        sum += 1.0/(num*2);
    }else{
        sum -= 1.0/(num*2);
    }
}

http://codepad.org/KgGAxKxS

Upvotes: 1

mathematician1975
mathematician1975

Reputation: 21351

In your loop you have this

k=+2;

so you assign the value 2 to k every iteration. You probably want

k+=2;

also take heed of the integer division problem highlighted in the other answer

Upvotes: 3

Michael Krelin - hacker
Michael Krelin - hacker

Reputation: 143209

Try 1./k — otherwise integer division of 1 by anything will yield zero. (and see the other answer about =+ vs += typo).

Upvotes: 7

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