Objective-C. 0 + 1/2 + 1/4 + 1/8 + 1/16 +...

Google knows too much. Actually, I was surprised to find out that I can check my math exercise without a calculator or another application. I have to learn Objective-C and now I do not see another way but make simple math exercises.

Here is a program calculating the same formula - sum of fractions 1/2, 1/4, 1/8, etc. The denominator is always 2 in power of n. If the n is big enough the result, the sum of this series should approach 1.

#import <Foundation/Foundation.h>
#import "Fraction.h"

int main (int argc, const char * argv[]) {
    NSAutoreleasePool * pool = [[NSAutoreleasePool alloc] init];
    
    Fraction *fraction = [[Fraction alloc] init];
    Fraction *sum = [[Fraction alloc] init];
    int n, i, pow2;
    
    [sum setTo: 0 over: 1];
    
    NSLog(@"Enter your value for n:");
    scanf("%i", &n);
    
    pow2 = 2;
    for (i = 1; i <= n; ++i)
    {
        [fraction setTo: 1 over: pow2];
        [sum add: fraction];
         pow2 *= 2;
    }
    
    NSLog(@"After %i iteration, the sum is %g", n, [sum convertToNum]);
    
    [fraction release];
    [sum release];
    [pool drain];
    return 0;
}

And here is the console:

This program uses the class Fraction declared in file Fraction.h:

#import <Foundation/Foundation.h>


@interface Fraction : NSObject {
    int numerator;
    int denominator;
}

@property int numerator, denominator;

-(void) print;
-(double) convertToNum;
-(void) setTo: (int)n over: (int)d;
-(void) add: (Fraction*) fraction;
-(void) reduce;

@end

and the class is implemented in Fraction.m:

#import "Fraction.h"

@implementation Fraction

@synthesize numerator, denominator;

-(void)print
{
    NSLog(@"%i/%i", numerator, denominator);
}

-(double)convertToNum
{
    if (denominator != 0)
        return (double) numerator / denominator;
    return 1.0;
}

-(void) setTo: (int) n over: (int) d
{
    numerator = n;
    denominator = d;
}

-(void)add: (Fraction*) fraction
{
    numerator = numerator * fraction.denominator + fraction.numerator * denominator;
    denominator = denominator * fraction.denominator;
    [self reduce];
}

-(void) reduce
{
    int u = numerator;
    int v = denominator;
    int temp;
    
    while (v != 0)
    {
        temp = u % v;
        u = v;
        v = temp;
    }
    
    numerator /= u;
    denominator /= u;
}


@end