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Mathematics
Mathematics
Problem
For real parameter
k
k
k
, define
a
n
(
k
)
=
{
1
n
,
n
even
,
−
k
n
,
n
odd
.
a_n(k)=\begin{cases}\dfrac{1}{n}, & n\text{ even},\\[6pt]-\dfrac{k}{n}, & n\text{ odd}.\end{cases}
a
n
(
k
)
=
⎩
⎨
⎧
n
1
,
−
n
k
,
n
even
,
n
odd
.
For which values of
k
k
k
does the infinite series
∑
n
=
1
∞
a
n
(
k
)
\displaystyle\sum_{n=1}^{\infty} a_n(k)
n
=
1
∑
∞
a
n
(
k
)
converge? a)
k
<
1
k<1
k
<
1
b)
k
=
1
k=1
k
=
1
c)
k
>
1
k>1
k
>
1
d) All real
k
k
k
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