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Math Help - prove a convergent sequence

  1. #1
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    prove a convergent sequence

    a1 = √3
    an+1 = √(3 + an)

    How do you prove that an is convergent?

    Would you find its limit by an tends to a (as n tends to inf.), so an+1 tends to a. Then solve for a by a2 = a + 3??
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  2. #2
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    Prove that a_n<a_{n+1}<3. Do this by induction.

    Then we know that an increasing bounded sequence converges.

    Then to find the limit solve this: L=\sqrt{3+L}
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  3. #3
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    Quote Originally Posted by Plato View Post
    Prove that a_n<a_{n+1}<3. Do this by induction.

    Then we know that an increasing bounded sequence converges.

    Then to find the limit solve this: L=\sqrt{3+L}


    thank you!! But how would you go about proving that by induction?
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  4. #4
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    Quote Originally Posted by pseudonym View Post
    thank you!! But how would you go about proving that by induction?
    Well prove that a_1 < a_2 <3.

    Then show that a_K<a_{K+1}<3 implies a_{K+1}<a_{K+2}<3.
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