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1. Consult a list of common power series to find the exact sum of the following series:
a. 1 - 1/3 + 1/5 - 1/7 + ··· + (-1)n (1/2n+1) + ···
b. n=0Σ∞ ((-1)nπ2n/32n(2n!))
2. Apply the Ratio Test to determine whether n=1Σ∞ (3n/n22n+1) converges.
3. Apply the Root Test to determine whether n=1Σ∞ (3n-1/2n+5)n converges.
4. Find the radius of convergence of the power series.
a. n=0Σ∞ (n!xn/2n)
b. n=0Σ∞ (x2n/(2n)!)
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1. A random number generator selects a sequence of 20 digits from {0, 1, . . . , 9}. What is the probability [2] that the sequence contains at least one 3? (Hint: consider the probability that the sequence contains no 3's.)
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