Prove that walk(n) = fn+1 for all n greater than or equal to 1

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Prove that walk(n) = fn+1 for all n greater than or equal to 1

Discrete Math
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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better formatting \[walk(n) = f _{n+1}\]
i know its an induction proof but the part im at is trying to show that walk(k+1) = [f _{k+2}\] and im assuming ive done everything correctly i just can think of how to manipulate the left hand side and make it look like the right hand side
\[walk(k+1) = f _{k+2}\] not sure what happened above but this is what im pretty sure im trying to prove

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