- #1
DivGradCurl
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How do I prove by mathematical induction that the sequence given by
[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?
[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?