At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

\[\text{Given} \ x_1 > 4, \]\[x_{n+1}=\frac{1}{2}x_n+\frac{8}{x_n}\]

In line 2 of my first reply, should I solve for x_n, or how should I set this up to plug in for n=1?

Yeah, I don't get it. Why are you allowed to substitute 2 for 8/x_n?

are you refering to first line ?

\[x_n\gt 4 \implies \dfrac{1}{x_n}\lt \dfrac{1}{4} \implies \dfrac{8}{x_n} \lt 2 \]

left hand side in your recent reply is same as \(x_{n+1}\)

we cannot use part \(b\) to prove part \(a\)
as we have used part \(a\) in proving part \(b\)

we must prove part \(a\) standalone

|dw:1444111567156:dw|

So i.) is just a given that x_1 > 4?

Yes, it works.

Induction step seems tricky though

I'll try the induction step after some time... going for lunch now..

|dw:1444114182268:dw|

|dw:1444114292088:dw|

thus proving your induction step

|dw:1444114363766:dw|

c) it goes to 4 ofcourse :)

|dw:1444115424905:dw|

|dw:1444115484266:dw|

for infinite times