Unformatted text preview: (a) [10 points] ∞ X n =1 n 2 + 1 n 4 + n (b) [10 points] ∞ X n =1 3 n 4 n5 5. [10 points] Write out the ﬁrst three partial sums ( s 1 , s 2 , and s 3 ) of the series ∞ X n =1 2 n n ! . 6. [10 points] Give an example of an inﬁnite series X a n which diverges, even though lim n →∞ a n = 0. 7. [10 points] Suppose a series ∑ a n has positive terms ( a n > 0) and its partial sums satisfy s n < 54 for all n . Explain why the series must be convergent....
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 Winter '98
 MathDep
 Math

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