The Clown Climbing the Stairs

A clown can climb a staircase either by one step or by two steps. For example, he can climb from the floor to the first step and then to the third, or he can climb from the floor to the first step, then to the second, and then finally to the third.

If a staircase has 10 steps, in how many ways can the clown climb it?

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Clarification:

  • When he climbs from the \({ 9 }^\text{th}\) step to the \({ 10 }^\text{th},\) he has climbed the whole stair; that is, the final step is the second floor.
  • The order in which he climbs the staircase matters!

Bonus: Generalize it.

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