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10sE2FirstFewProblems

# 10sE2FirstFewProblems - Prof Girardi Math 142 Typical First...

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Prof. Girardi Math 142 Typical First Few Problems on Sequences & Series Exam If you do not make at least a 50% on this exam’s first few problems , then your total exam score will be only as many points was you managed to get on the first few problems . Here are some typical first few problems . 1. Fill-in-the blanks/boxes. All series are understood to be X n =1 . Hint: You should NOT write the words absolute nor conditional on Problem 1! 1a. Sequences (Afterall, this is needed for Geometric Series!) Let -∞ < r < . (Fill-in-the blanks with exists or does not exist, i.e. DNE ) If | r | < 1, then lim n →∞ r n If | r | > 1, then lim n →∞ r n If r = 1, then lim n →∞ r n If r = - 1, then lim n →∞ r n 1b. Geometric Series where -∞ < r < . The series r n converges if and only if | r | diverges if and only if | r | 1c. p -series where 0 < p < . The series 1 n p converges if and only if p diverges if and only if p 1d. Integral Test for a positive-termed series a n where a n 0. Let f : [1 , ) R be so that a n = f ( ) for each n N f is a function f is a function f is a function .

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