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Answer these questions using the Federal Reserve Bank of St. Louis’s.pdf
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### answer as true or false if true explain why if false provide a count.pdf

1. answer as true or false if true explain why if false provide a counter example ( do not correct a false statement) a) let (a_n)_neN be a sequence that possesses a convergent subsequence. Then (a_n)_neN is bounded b) let (an)nEN and (bn)nEN be sequences that both diverge. Then (a_n + b_n)_neN is also divergent. c) let x> 0 Then x + (1/x) > = 2 Solution a. FALSE. Consider teh sequence an = n if n is even = 1/n if n is odd. Clearly the odd subsequence is convergent but the sequence itself is not bounded. b. FALSE. Let an = n for all n, bn = -n for all n. Clearly both diverge. But their sum is the constant sequence cn = an+bn = 0 which is obviously converget. c. TRUE. x + 1/x - 2 = (x2- 2x + 1)/x = (x-1)2/x>0 since teh numerator is a square and teh denominator is positive by assumption.
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