power series 1 what is the difference between a sequence and a series

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Power Series
1. What is the difference between a sequence and a series?
2. What is a power series? How is it different from and similar to a series?
3. Find the radius and interval of convergence for
∞
Σ
k=0
2k
kk
4. Find the radius and interval of convergence for
IM 8
5
(x — 7) k.
k3k 5. Find the radius and interval of convergence for
6. Find the derivative of
k=0
k!
k=0
k!
-(x+3)k.
In k
7. Write out the series
k=0
2k
k!
xk
term by term and take the derivative term by term. Com-
pare your answer to the above.
Page 2 ∞
8. Find an antiderivative of
-x2k
In k
k=0
9. Indicate if the following are always true or may be false.
If
(a)
(b)
(c)
If
oak (x-1)* converges when x =
k=0
If Σkoak (x-1)
k=0
oak (x-1)
k=0
4, then it must converge when x = = 3.
converges when x = 4, then it must converge when x = −1.
converges when x = 4, then it must converge when x = -2.
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