Coverge Crossword
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
 
 
Down: 1) blank2) Prove: ____ let epsilon >0 choose n>____ there if n>=N we know______________ For n>=N consider: |an-A|=____________ Thus, by the defn of convergence we can conclude that__________3) Prove: ___________ choose e<_____ let Q={A-e, A+e } such that Q is a neighborhood consider: { , } =Q Clearly Q excludes ___ for all n<= ____ (epsilon value) Now consider any A in the neighborhood {A-___, A+__} Since the neighborhood is ___ (add the blanks from A) and is <___ which equals _____(distance) it is clear the neighborhood cannot contain both ____ & ___. since the distance between them is ____ .5) ldkf7) dslknfsdlkfj8) blank Across: 4) A convergent sequence is a sequence that for any positive integer we choose we can always find a term in the sequence that gets closer and closer to a common value.6) Prove:____ let e>0 choose N=S then if n>=N we know that n>= S For n>=N consider: |an-A|=|an-S|=|S-S|=09) a sequence {an} for n=1 to infinity converges to a real number A iff for each epsilon >0 there is a positive integer N such that for all n>=N we have |an-A|< epsilon.10) blank
 

 

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