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# P2 Question watch

1. un = 1 + √(un)

u1 = 16

Prove that the limiting value of the sequence is

a + b√5

where a and b are rational numbers to be found

Cheers!

Btw, if you have wasted all your time re-learning everything you've ever done for biology then find out you have no time to revise p2 - i know the feeling!!!
2. u1=16
u2=5
u3=3.236

so

u3=1+root 5

and u3 isnt a whoel number, so is this the limit?
3. no... because there's u4, u5, u6, u7...
4. (Original post by Revenged)
un = 1 + √(un)

u1 = 16
Is this supposed to be a recurrence relation.. ... in which case it probably should look more like un+1=1 + √(un) to make sense
5. Let L be the limit of Un as n -> ∞

Then Un+1 ≈ Un as n -> ∞

Un+1 = 1 + √Un

as n -> ∞

L = 1 + √L
(L-1)² = L
L² - 2L + 1 = L
L² - 3L + 1 = 0
L = (3 ±√(3² - 4.1.1))/2.1
L = (3 ±√(9 - 4))/2
L = 3/2 + √5/2
===========
a = 3/2, b = 1/2
============
6. thanks, doubt if i'll get anything as bad as that tomorrow though!

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