12. (a) Write out the first 10 terms of {an} where a = 10 and an+1...

 

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12. (a) Write out the first 10 terms of {an} where a = 10 and an+1 = an + 1. (b) Based on your results in part (a), what values appear to bound this sequence above and below? (c) Prove that this sequence is bounded below by 2. (Explain how we know that an 2 for each n) (d) Prove that this sequence is nonincreasing. (Explain how we know that an+1 an for each n) (e) Based on your results from (c) and (d), what can we conclude about this sequence? 12. (a) Write out the first 10 terms of {an} where a = 10 and an+1 = an + 1. (b) Based on your results in part (a), what values appear to bound this sequence above and below? (c) Prove that this sequence is bounded below by 2. (Explain how we know that an 2 for each n) (d) Prove that this sequence is nonincreasing. (Explain how we know that an+1 an for each n) (e) Based on your results from (c) and (d), what can we conclude about this sequence?