Consider the possible structures of the N ion shown below + N=N=N-NEN 2 :N-NEN-NEN NEN-N-NEN N-N=N=N=N 5 NEN-N-N-N N=N-NEN-N: Based on formal charges, which structure ( #2 or #3) is the less likely arrangement of the electrons? Based on formal charges, which structure (#5 or #6 ) is a more likely arrangement of the electrons? What is the formal charge on the central nitrogen atom in structure 1? How many of the structures above represent likely arrangements for the electrons...
(2) (a) Let {n}nen be a sequence of complex numbers. Show that if lim, toon = 2, then lim 21+z2+ + + Zn 100 (b) Using (a), find the limit limn7 (m_ +i i zm).
(2) Consider the following examples. (a) Let A = n.) for each neN. What is Ain A, for any i,j EN? What is an An? (b) Let Bn = (0,1/n) for each neN. What is Bin B; for any i, j e N? What is aan Bn? (c) What's the deal with these examples? Do they relate to Helly's Theorem? What might be going wrong here?
Let (an)nen be a bounded sequence in R. For all n e N define bn = sup{am, On+1, On+2,...}. (You do not have to show that the supremum exists.) (a) Prove that the sequence (bn)nen is a monotone sequence. (b) Prove that the sequence (bn)nen is convergent. (c) Prove or disprove: lim an = lim bre. 100 000
5. Let fn(x) = x"/n on [0, 1]. Show that (fr)nen converges uniformly to a differentiable function on [0, 1], but (f%) does not converge uniformly neN on [0, 1].
For each . Find the intersection of and prove. Please show and explain steps. neN. An = zeR: (1/n) <<<1+(1/n) We were unable to transcribe this image
Q2 (10 points) Vn2 + 4 – n, n E N. 2. Let (an) neN be the sequence with a, (a) Prove that lim,→0 an 0. lim,-00 bn, and prove the limit exists, by using the definition. (b) Let bn = n an . Find L =
2. Let {xn}nEN be a sequence in R converging to x 0. Show that the sequence R. Assume that x 0 and for each n є N, xn converges to 1. 3. Let A C R". Say that x E Rn is a limit point of A if every open ball around x contains a point y x such that y E A. Let K c Rn be a set such that every infinite subset of K has a limit...
real analysis questions Find the interior of the following sets. (1): {1/n: neN}: (2): (0,5) (5, 7); (3): {re Q:0<r <2}. Classify each of the following sets as open, closed, or neither. (1): {: | - 51 < 1}; (2): {x: (x-3) > 1}; (3): {:13 -4)<4}.
Test the series for convergence or divergence. n + 1 12. § (-1*me* nen n= 1