a_1 = a, a_(n+1) = SQRT(a + a_n)

[dts5044]

let a[sub:9a1o9m9x]1[/sub:9a1o9m9x] = a, where a > 0 (constant), and a[sub:9a1o9m9x]n+1[/sub:9a1o9m9x] = SQRT(a + a[sub:9a1o9m9x]n[/sub:9a1o9m9x]) for n >=1, is the sequence (a[sub:9a1o9m9x]n[/sub:9a1o9m9x]) n>=1 monotonic, bounded, convergent? If yes, find its limit

 

[stapel]

let a[subybii2f5]1[/subybii2f5] = a, where a > 0 (constant), and a[subybii2f5]n+1[/subybii2f5] = SQRT(a + a[subybii2f5]n[/subybii2f5]) for n >=1, is the sequence (a[subybii2f5]n[/subybii2f5]) n>=1 monotonic, bounded, convergent? If yes, find its limit

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

Eliz.

 

[Deleted member 4993]

let a[sub:vz003dh1]1[/sub:vz003dh1] = a, where a > 0 (constant), and a[sub:vz003dh1]n+1[/sub:vz003dh1] = SQRT(a + a[sub:vz003dh1]n[/sub:vz003dh1]) for n >=1, is the sequence (a[sub:vz003dh1]n[/sub:vz003dh1]) n>=1

monotonic, <<< What is the definition - how would you prove it?

bounded, <<< What is the definition - how would you prove it?

convergent? <<< What is the definition - how would you prove it?

If yes, find its limit