21.1.7. Definition of Bad Sequence

Try these first

1. 1.

   Define a bad sequence in your own words.

   Hint

   Consider sequences of 1s and -1s.

2. 2.

   Provide an example of a valid sequence.

   Hint

   Check partial sums while scanning.

3. 3.

   What defines a bad sequence in terms of its sum?

   • All partial sums are positive
   • At least one partial sum is negative
   • All sums are zero

   Hint

   Remember the definition!

4. 4.

   True or False: The set A contains all sequences of equal numbers of 1s and -1s without restrictions.

   • True
   • False

   Hint

   Think about how we define these sets.

5. 5.

   Given a bad sequence with 4 pairs of 1s and -1s, demonstrate step-by-step the reflection method and find valid sequences.

   Hint

   Mark the negative point clearly before reflecting.

6. 6.

   Explore a relationship between sets A and B using numerical examples for n=3 and calculate corresponding Catalan numbers.

   Hint

   Use combinations formulas and think about counts.