Fill in the blanks in the following proof (in attachment), which shows that the sequence defined by the recurrence relation for each integer k ≥ 2
satisfies the following formula. for every integer n ≥ 1
Proof (by mathematical induction):
Suppose , , , ... is a sequence that satisfies the recurrence relation for each integer k ≥ 2, with initial condition .
We need to show that when the sequence , , , ... is defined in this recursive way, all the terms in the sequence also satisfy the explicit formula shown above.
So let the property P(n) be the equation . We will show that P(n) is true for every integer n ≥ 1.