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Question
Mathematics
The limit of ∑ limits1000 n-1 (-1)n xn as x→∞
Q. The limit of
n
−
1
∑
1000
(
−
1
)
n
x
n
as
x
→
∞
2406
204
WBJEE
WBJEE 2013
Limits and Derivatives
Report Error
A
does not exist
0%
B
exists and equals to 0
22%
C
exists and approaches to
+
∝
78%
D
exists and approaches
−
∞
0%
Solution:
x
→
∞
lim
n
=
1
∑
1000
(
−
1
)
n
x
n
=
x
→
∞
lim
{
−
x
+
x
2
−
x
3
+
x
4
+
…
+
x
1000
}
=
x
→
∞
lim
(
−
x
)
⋅
{
(
−
x
−
1
)
(
−
x
)
1000
−
1
}
=
x
→
∞
lim
x
+
1
x
1001
−
x
=
x
→
∞
lim
1
+
(
x
1
)
x
1000
−
1
=
+
∞