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## Main Question or Discussion Point

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

[tex]a_1=1[/tex]

How should I prove that [tex]a_{n+1}>a_n[/tex]

for all n, ?

I have tired to use counter example,

assuming

[tex]a_n>a_{n+1}[/tex]

then contradiction appears,

but I found that what I was doing is just to counter "for all n"

How should I prove that

[tex]a_{n+1}>a_n[/tex] ,for all n ?

[tex]a_1=1[/tex]

How should I prove that [tex]a_{n+1}>a_n[/tex]

for all n, ?

I have tired to use counter example,

assuming

[tex]a_n>a_{n+1}[/tex]

then contradiction appears,

but I found that what I was doing is just to counter "for all n"

How should I prove that

[tex]a_{n+1}>a_n[/tex] ,for all n ?