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Why is it required that a recursion be bounded?

For example given $U_n = aU_{n-1} + c$ where $a$ and $c$ are constants. Why is it necessary that you specify that $n>1$ in your response.

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    Where did the requirement come from ? – 2017-02-19
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    Probably because in the book you are using they treat sequences starting at 1, then the relation can only be true for $n>1$, otherwise on the rhs you'll get $U_0$. Just a matter of notation. – 2017-02-19

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