BC Calc III
Quiz 9.4 - 9.5
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#1 (4 pts) Find the interval of convergence of (No work necessary).

a.
b.
c.
d.
xn

n
n 0 n  4

(x  3)n

3n
n 0

( x  2) n

n2
n 0

(1)n ( x  3)n

n  5n
n2
Interval of convergence =
Interval of convergence =
Interval of convergence =
Interval of convergence =
2n ( x  2) n
. (Show all work).

n2
n 0

#2 (5 pts) Find the interval of convergence of
BC CALC III

#3(8 pts). Look at the series

n 1
(1)n
.
n  3n
a. Show that this series converges.
b. Find a value for n such that Sn is within .001 of the actual sum.
#4(5 pts). Determine whether the following series converges conditionally, converges
absolutely, or diverges? Show all steps/explain.


n 1
(1)n  n ! nn
(2n)!
BC CALC III

#5(2 pts each) Suppose that the power series
 a ( x  1)
n0
n
n
converges if x  3 and diverges if
x = 8. Indicate whether the following statements must be true, which may be true, and which
cannot be true. Justify your answers.
a. The power series converges if x = 2.
b. The power series converges if x  4
c. The power series diverges if x = 5.
d. The power series converges absolutely if x = 4.
1,000,000
#6 (2 pts) Estimate

n 1
BC CALC III
1
to the nearest whole number. Explain all analysis clearly.
n