Determine this sequence increasing or decreasing

[e179285]

A sequence (a_n) is recursively defined by a₁ = 1 and
a_n+1 =1 /(2+a_n ) for all n≥1

I'll prove this sequence is convergent by monoton sequence theorem.ı can find ıt is bounded but ı cannot decide it is monoton because when ı write its terms,Its terms are increasing sometimes decreasing sometimes.

How can ı prove it is increasing or decreasing?

 

[clamtrox]

How can ı prove it is increasing or decreasing?

For what value of a_n would it be stationary, ie. a_n+1 = a_n?

 

[mtayab1994]

Do an+1-an and you'll have to combine it into one fraction and then do some factoring and you'll see if it's decreasing or increasing.