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Mathematics
Mathematics
Problem
Consider the two power series, each centered at
x
=
−
1
x=-1
x
=
−
1
: I.
∑
n
=
0
∞
(
x
+
1
)
n
3
n
\displaystyle \sum_{n=0}^{\infty} \frac{(x+1)^{n}}{3^{n}}
n
=
0
∑
∞
3
n
(
x
+
1
)
n
II.
∑
n
=
1
∞
n
(
x
+
1
)
n
5
n
\displaystyle \sum_{n=1}^{\infty} \frac{n(x+1)^{n}}{5^{n}}
n
=
1
∑
∞
5
n
n
(
x
+
1
)
n
What is the largest interval (centered at
−
1
-1
−
1
) on which both series converge? a)
(
−
6
,
4
)
(-6,4)
(
−
6
,
4
)
b)
[
−
4
,
2
]
[-4,2]
[
−
4
,
2
]
c)
(
−
4
,
2
)
(-4,2)
(
−
4
,
2
)
d)
(
−
5
,
3
)
(-5,3)
(
−
5
,
3
)
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