Recurrence Relations · Recursive Definitions

Lesson 7

Nikolai Chukhin · Alexander S. Kulikov

By listing the first few terms of this sequence, you can easily recognize powers of two.

At this point, it is natural to conjecture that \(L(n)=2^{n-1}\), which can then be easily established by induction.

Another way is to unfold the recurrence relation: \[L(5)=2L(4)=2^{2}L(3)=2^{3}L(2)=2^{4}L(1)=2^{4}.\]