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The Review Test of Chapter 7

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The Review Test of Chapter 7- Due 4/23/08

1. (5pts) Determine if the sequence converges or diverges. If it converges, find the limit.

Hint: Sec 7.1 #65

an= 1

√n

n

2. Determine the convergence or divergence of the series (a) (5pts)

∑∞ n=1

(−1)n− (1 3)n (b) (5pts) Hint: Prob 1

∑∞ n=1

1

√n

n

(c) (5pts) (Comparison Test or Limit Comparison Test)

∑∞ n=1

n + 1

√n5− 2n + 2

(d) (5pts) (Alternating Series Test)

∑∞ n=1

(−1)n+1 1 ln(n + 1)

3. (5pts) Use the Integral Test to test the convergence of the series

∑∞ k=2

1 k ln k

4. (10pts) Determine the radius and interval of convergence of the power series.

∑∞ n=1

(x− 5)n n· 3n 5. (a) (5pts) Find the Maclaurin series of f (x) = 1+x1 ,

(b) (5pts) Find the Maclaurin series of f (x) = ln (1 + x),

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