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C Brain Teasers: Exercise Your Mind

Discussion: This Should Ring a Bell

Understand how C code uses loops to calculate sums of two harmonic series types: divergent and convergent. Learn to observe output patterns and grasp the math behind harmonic sequences, including their convergence and divergence behaviors, through practical coding examples.

We'll cover the following...

Run the code

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

C
#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, 1/21/2 ...