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Math 241 Name: Quiz 3 1. [6 points] State whether the given series converges or diverges. If it does converge, state whether it converges absolutely. You do not need to justify your answers. (a) (−1)n ∑ 2 n=1 n (b) (−1)n ∑ √n n=1 (c) (−2)n √ n n=1 ∞ ∞ ∞ ∑ 2n ∑ 3n(n + 1) xn. n=0 ∞ 2. [4 points] Find the radius of convergence of the power series 3. [8 points] Find the first three terms of the Taylor series for the function f (x) = √ x centered at a = 4. 4. [8 points] Evaluate the following limit: √ 1 − cos x . lim x→0 x 5. [14 points] Write the indefinite integral Z ln 1 + x3 dx as an infinite series. Express your answer in summation notation.