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Alternating Series - Calculus - Quiz, Exercises of Calculus

Aliah UniversityCalculus

This is class quiz. Its from Calculus class. Some key points are: Alternating Series, Comparison, Geometric Series, Integral, Ratio, Absolute Test, Converges or Diverges

Typology: Exercises

2012/2013

Uploaded on 03/16/2013

ranga
ranga 🇮🇳

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Name:
Math 106A: Winter 2012
Quiz 3: March 30
Correct answers accompanied by incorrect or incomplete work will not receive full credit.
Good Luck!
Convergence Tests
•Geometric Series
•nth Term
•Comparison
•Integral
•pTest
•Ratio
•Alternating Series
•Absolute Test
1. For each of the following series determine whether it converges or diverges. Carefully justify your
answers.
(a)
∞
X
n=1
n
3n+ 1
(b) 1
3−1
9+1
27 −1
81 +· · ·
pf2

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Name:

Math 106A: Winter 2012

Quiz 3: March 30

Correct answers accompanied by incorrect or incomplete work will not receive full credit. Good Luck!

Convergence Tests

  • Geometric Series
  • nth Term
  • Comparison
  • Integral
    • p Test
    • Ratio
    • Alternating Series
    • Absolute Test
  1. For each of the following series determine whether it converges or diverges. Carefully justify your answers.

(a)

∑^ ∞

n=

n 3 n + 1

(b) 1 3

+^1

OVER

  1. Show that each of the following series converges. Then find good upper and lower bounds for each series.

(a)

∑^ ∞

n=

(−1)n+ 2 n − 1

(b)

∑^ ∞

k=

(k + 2)^2