Answers by visitors named: Sarita

thank you! Additionally, 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?

But why would you look for the derivative to go to zero? Does it have to do anything with the theorem: If summation of a_n converges then limit_(n-->infinity) of a_n = 0. If so, what would the limit be approaching? 10 or infinity? But if not, then what theorem would we use? I know you explained about the larger n for the derivative, but I do not understand how that relates to one of the theorems.

But doesn't it converge to infinity and not 0?

we want it to converge to 0 right? But does it even converge if it goes to infinity, or is that divergence?

Do you do the limit on the derivative? Or is there another way to prove convergence with a theorem of some sort?

Which theorem, together with the results of parts a and b, will guarantee convergence? Would it be the convergent sequences are bounded theorem, where if {a_n} converges, then {a_n} is bounded, or would it be the bounded monotonic sequences converge theorem, where 1) if {a_n} is increasing and a_n(</=)M for all n, then {a_n} converges and lim_(n-->infinity)a_n(</=)M, and 2) if {a_n} is decreasing and a_n(>/=)m for all n, then {a_n} converges and lim_(n-->infinity)a_n(>/=)m? or is there another one?

So, what would be the exact limit of the sequence defined in part c? But it says to square the recursive equation and take limits using some limit theorems. How do you do that?

Equation of motion for he truck: s=ut Equation of motion for the car: s=1/2at^2 the second solution gives , s=2u^2/a = 2*10^2/2 = 100m