How do I prove by mathematical induction that the sequence given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex] a_{n+1}=3-\frac{1}{a_n} \qquad a_1=1 [/tex]

is increasing?

The difficulty in finding it myself is that recursive sequences are not familiar to me---i.e. usually, I am able do the following steps without a problem:

(A) Show n=1 gives a true statement.

(B) Assume it is true for n=k.

(C) Get to n=k+1 and complete the proof.

... but this is not a regular sequence. Can anyone give me a tip?

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# Mathematical induction/recusive sequences - just need a hint

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