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December 22, 2014

December 22, 2014

Posted by **Sarita** on Saturday, April 3, 2010 at 1:15am.

B) So once that is found, then how can you prove that if 0(<or=)u(<or=)v(<or=)10, then 0(<or=)sqrt(u+1)(<or=)sqrt(v+1)(<or=)10?

C) They give a recursively defined sequence: a_1=0.3; a_(n+1)=sqrt((a_n)+1)for n>1

How do you find out the first five terms for it. then prove that this sequence converges. What is a specific theorem that will guarantee convergence, along with the algebraic results of parts A and B?

D) How do you find out the exact limit of the sequence defined in part C? Are you supposed to square the recursive equation and take limits using limit theorems? If so, then which are these theorems?

Thank you very much.

- calculus -
**Damon**, Saturday, April 3, 2010 at 8:43pmI answered this below after I did the first two.

- calculus -
**Damon**, Saturday, April 3, 2010 at 8:47pmcalculus - Damon, Saturday, April 3, 2010 at 7:26pm

.3

sqrt 1.3 = 1.14

sqrt 2.14 = 1.46

sqrt 2.46 = 1.57

sqrt 2.57 = 1.60

hmmm, not getting bigger very fast.

let's see what happens to the derivative for large n

.5/sqrt(x+1)

ah ha, look at that. When n gets big, the derivative goes to zero. So the function stops changing.

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