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Math Help - Prove that this converges

  1. #1
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    Prove that this converges

    Let [a,b] be a closed interval in \mathbb R, and suppose that { \ s_n}, \ n \geq 1 is a sequence within [a,b]. Prove that the sequence { s_n/n}, \ n \geq 1, converges.

    Anyone know how to do this problem? thanks in advance guys.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Cato View Post
    Let [a,b] be a closed interval in \mathbb R, and suppose that { \ s_n}, \ n \geq 1 is a sequence within [a,b]. Prove that the sequence { s_n/n}, \ n \geq 1, converges.

    Anyone know how to do this problem? thanks in advance guys.
    note that the s_n's are bounded.
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  3. #3
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    We have
    \frac{a}{n}\leq \frac{s_n}{n}\leq \frac{b}{n}
    then use squeeze theorem
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  4. #4
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    Why a/n and b/n
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Cato View Post
    Why a/n and b/n
    it is within the interval [a,b]. so the smallest an element of the sequence can be is a, while the largest it can be is b
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  6. #6
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    Thanks guys
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