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Final

# COMPLETE Calculus II for Math and Science Majors Notes (90% on final exam)

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School
Boston College
Department
Mathematics
Course
MATH 1103
Professor
All
Semester
Winter

Description
Given Series ∑ an… Geometric: Telescoping: Harmonic: n ∑ ar ∑ 1 ∑ 1 n(n+1 ) n CONV:    If  ∣r<1 , conv. to  Converges to 1 Diverges to  a ∞ 1−r P­Series: Alternating Series Test: a=FirstTerm 1 ∑ P ∑ −1 )−1bn DIV:    If r≥1 n CONV:    If  Converges If… Divergence Test: p>1 i. b n+1b n lim a … DIV:    If p≤1 n→∞ n ii. lim bn=0 DIV:    If limit DNE or  n→∞ is a finite number Integral Test: ∞ If lim n =0… Let  a =f (x)D and suppo∫e  (x)dx  diverges n→∞ n 1 f (x) is positive,  ∞ MUST TRY ANOTHER TEST!    decreasing, aCONV:    If s∫onf (x)dx converge 1,∞)   1 Comparison Test: Limit Comparison TesIf c is(0,∞) , both series  suppose  ∑ a n  and  ∑ bn   (If 0≤an≤bn) are series with positive terms erge or diverge b and tha  If  c=0  and  b   If  ∑ n  converges,
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