(3) IF THE SEQUENCES {x, + y} AND {X- BOTH CONVERGE THEN THE SEQUENCES (X) and...
Let an and br be sequences. Prove that sequences an and by both converge iff both an + br and an - bre converge.
nees in (Mod) that converge to (2) Let (an) and (y) be sequences in & and y respectively. Prove that d(x,y) d(x,y). If SCM is bounded, prove that the diameter o the diameter of cics) are equal. I the diameter ofs and
3. (18 pts) Determine if the following sequences converge or diverge. For those that converge, determine the limit of the sequence. Make sure to fully justify your answer! arctan(n) (a) an= n In +3 (b) bn = (-1)" n² + 40 + 4)
, { x,1. {%) and {4) hat converge almost surely to a,b,c onsider three sequences of random variables respectively. Prove that a.s , { x,1. {%) and {4) hat converge almost surely to a,b,c onsider three sequences of random variables respectively. Prove that a.s
6. ... / 6 points) Determine if the following sequences converge or diverge. If they converge, give the limit. (a) an = (-1)" n+1 n (b) an = n In(n)
Pt 1 pt 2 pt 3 pt 4 Please Answer every question and SHOW WORK! Determine whether the series n-1 Σ (2n)! 2". (2n! converge or diverge 1. both series converge 2. only series II converges 3. only series I converg es 4. both series diverge Determine whether the series 2! 1515.9 1-5.9-13 3! 4! 7m 1.5.9..(4n -3) is absolutely convergent, conditionally con- vergent, or divergent 1. conditionally convergent 2. absolutely convergent 3. divergent Determine which, if any, of the...
Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge. 2Ti3 1 Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge. 2Ti3 1
1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an= n-cos(n) 4n2-7 Tn (d) { } 2. Prove that the following sequences diverge. (Def 7.10 pg 596) READ Sequences that Diverge to oo or-oo (b) ann infinity. Hint: Provide an M -N proof that an approaches 1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an=...
Find all the values of x such that the given series would converge. (-1)"x" 11(n2 +9) The series is convergent from x= left end included (enter Y or N): tox= right end included (enter Y or N):
(1 point) Find all the values of x such that the given series would converge. (-1)"x" 6" (n2 + 8) n=1 The series is convergent from x = left end included (enter Y or N): to x = , right end included (enter Y or N):