IA Infinite surds

[SharkSpider]

This is actually a pretty easy question. Just stop looking at the first terms and start looking at the infinite-th terms instead. It's been a long while since I've done IB so I don't know how much I'm allowed to say, but you really shouldn't need anything more than that to find the answer.

[Tilia]

Don't start threads about a IA topic, if there already exists one thread about it.

[Msukiddo]

Well im doing the same internal assessment but im struggling on finding the formula

I'm doing the infinite surds Math SL internal assessment... (Gags) One of the requirements is that i "use the results to find the exact value for this infinite surd."

sqrt(K+sqrt(K+sqrt(K+sqrt(K........ (sqrt = square root/ surd)is the sequence, so the recursive formula is a_n+1=(1+a_n)^1/2

The only "exact value" i know of for a sequence is the sum of an infinite geometric sequence, but my teacher pretty much said the general statement was meant to stay recursive. Plus, i've been doing regressions all day based on the first ten terms, and i'm fairly sure that looking for a geometric sequence is not what i'm supposed to be doing. Anyone have any ideas on what i should be doing?

[Dhara]

I have to do a practice portfolio on this stuff. And I need to find a formula a(sub)n+1 in terms of a(sub)n

I have to calculate the decimal values of the firs ten terms of the sequence then plot the relation between n and a. And I have to describe what this suggests the value of a(sub)n - a(sub)n+1 is when n gets very large.

I have to do this for sqrt(1+sqrt(1+sqrt(1 etc.. and as well as 2.

Then I have to conisder the general surd of k. I have to find an ex[ression for this.

I NEED HELP!