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.