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L17 Series Part II

# L17 Series Part II - x for which the following series...

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Lecture 17: Series (II) Telescoping Series 1. Find Partial Fraction 2. Compute S n 3. Find lim n !1 S n 1

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Determine if the following series converge. If converge, ±nd the sum: ex. 1. 1 X n =1 1 n ( n + 1) 2
ex. 2. 1 X n =1 ln ± n n + 1 ² 3

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Theorem: If P a n and P b n are both convergent series,then so are P ca n ; P a n ± b n ; and P ca n = c P a n ; P a n + b n = P a n + P b n ex. 3. 1 X n =1 ± 3 n ( n + 3) + 1 2 n ² 4
ex. 4. 1 X n =1 2 n 2 + 4 n + 3 5

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NYTI: 5. Use partial fractions to ±nd the sum of the series 1 X n =2 1 n 3 ± n : ( 1 4 ) 6
6. Find the values of
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Unformatted text preview: x for which the following series converges. Find the sum of the series for these values of x . 1 X n =0 ( x + 3) n 2 n ( ± 5 < x < ± 1 ; converges to 2 ± 1 ± x ) 7. Sum of 2 divergent series diverges. True or Falso? 8. Sum of a divergent and a convergent series must diverge. True or False? 7...
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