I'm sorry. That's the whole thing now.
I didn't realize that you needed the a,b,c,d parts to do the first part, I thought you had to inductively define Sn and then, using that definition, do the rest.
Let S1=1 and inductively define the sequence (Sn) so that Sn+1 = \sqrt{Sn + 1} for n\in Natural Numbers.
(a) Prove that Sn is a monotonically increasing sequence.
(b) Prove that Sn is a bounded sequence.
(c) Prove that Sn converges.
(d) Prove that lim(Sn)=\frac{1}{2} (1 + \sqrt{5} )
Homework Statement
Let S1=1 and inductively define the sequence Sn so that Sn+1 = \sqrt{Sn + 1}
Homework Equations
The Attempt at a Solution
I'm not sure what it means to "inductively define".
I think it wants me to come up with an equation for Sn by using Sn+1.
Does...
Figured it out! Thanks anyway :).
I was on the right track, all I did after that was square both sides of that last equation I had... and then it was clear from there!
I don't know if I'll get in trouble for this, but I just wanted to bring this back to the top before its pushed onto page 2 and forgotten... if that's not allowed just let me know, haha. Sorry.
Okay, so I've been playing around with stuff and this is what I've got:
Earth Frame:
tx=x/c because it's the amount of time it takes for the signal to reach the students.
so x= c(tx)
but x=vt also because t=x/v is the amount of time it takes the students to travel distance x...
Umm..
Earth Frame:
at time t=0, the first signal is sent.
at time T the second signal is sent.
at time t the second signal is received by the spaceship. At this time both the spaceship and the light signal have traveled x.
Spaceship Frame:
at time t=0 the first signal is recieved.
at...
Homework Statement
A physics professor on Earth gives an exam to her students who are on a spaceship traveling at speed v relative to Earth. The moment the ship passes the professor she signals the start of the exam. If she wishes her students to have time To (spaceship time) to complete the...
Hello. I'm currently an honours physics student in the second year of a BSc who is not enjoying herself.
I LOVED my introductory physics courses throughout high school and my first year of university. I thought it was amazing that almost everything we encounter during our day-to-day lives...
Electric potential of cylindrical conductor placed in a cylindrical conducting shell
Homework Statement
A cylindrical conducting shell is placed concentric with a cylindrical conductor. Assume that a total charge density λ0 = 2.60 µC/ m is placed on the inner...
I have the same question with different numbers and I have a question about it.
deltaV = - E x d for a uniform electric field
My assignment accepted a positive answer. What happened to the negative sign?
Thanks :)
Yeah, it is a question about the conservation of angular momentum haha... and yeah, I read a question that was almost the same as mine somewhere else on the forums and it talked about point mass, but I don't think our teacher has discussed that yet. I don't know how to find the moment of inertia...