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.

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.