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Mathematics
Mathematics
Problem
Which of the following statements is NOT required for the convergence of an alternating series of the form
∑
n
=
1
∞
(
−
1
)
n
a
n
\sum_{n=1}^{\infty} (-1)^{n} a_n
∑
n
=
1
∞
(
−
1
)
n
a
n
? a)
a
n
+
1
≤
a
n
a_{n+1}\le a_n
a
n
+
1
≤
a
n
for all sufficiently large
n
n
n
. b)
a
n
>
0
a_n>0
a
n
>
0
for all sufficiently large
n
n
n
. c)
∑
n
=
1
∞
a
n
\displaystyle \sum_{n=1}^{\infty} a_n
n
=
1
∑
∞
a
n
converges. d)
lim
n
→
∞
a
n
=
0
\displaystyle \lim_{n\to\infty} a_n = 0
n
→
∞
lim
a
n
=
0
.
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