For each of the following recurrence relations write out, Mathematics

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For each of the following recurrence relations write out

For each of the following recurrence relations, write out the first several terms of the sequence (at least five) and use this to find a closed form for the sequence. Then prove that each conjectured closed form is correct. (Is there a flashing sign in your head that indicates a fruitful approach?)

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Mathematics: For each of the following recurrence relations write out

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