C Brain Teasers: Exercise Your Mind/

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Discussion: This Should Ring a Bell

Discussion: This Should Ring a Bell

Execute the code to understand the output and gain insights into series summation.

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Run the code

Now, it's time to execute the code and observe the output.

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#include <stdio.h>
int main()
{
  const int limit = 1000;
  int x;
  float t;
  /* divergent */
  t = 0.0;
  for(x=1; x<=limit; x++ ) t += 1.0 / (float)x;
    printf("Divergent: %.4f\n", t);
  /* convergent */
  t = 0.0;
  for(x=1; x<=limit; x*=2 ) t += 1.0 / (float)x;
    printf("Convergent: %.4f\n", t);
    
  return(0);
}

Understanding the output

The code calculates the sum of two types of harmonic series, divergent and convergent:

Divergent: 7.4855
Convergent: 1.9980
Code output

While these values may not seem frightening, the math behind them is considered terrifying to some.

Harmonic series

Like the Fibonacci sequence, a harmonic sequence consists of the sum of values. But for a harmonic series, these are a series of fractions that follow a pattern. When all the fractions are added together, they either diverge and increase in value, or they converge by getting closer to a specific value.

The first loop in the given code represents a divergent harmonic series. It’s the sum of values 1/11/1 ...