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Mathematics
Problem
For the series
∑
k
=
1
∞
a
k
\displaystyle\sum_{k=1}^{\infty} a_k
k
=
1
∑
∞
a
k
, which of the following correctly defines the
n
n
n
th partial sum
S
n
S_n
S
n
? a)
S
n
=
∑
k
=
n
∞
a
k
S_n=\displaystyle\sum_{k=n}^{\infty} a_k
S
n
=
k
=
n
∑
∞
a
k
b)
S
n
=
∑
k
=
1
n
a
k
S_n=\displaystyle\sum_{k=1}^{n} a_k
S
n
=
k
=
1
∑
n
a
k
c)
S
n
=
lim
k
→
∞
a
k
S_n=\displaystyle\lim_{k\to\infty} a_k
S
n
=
k
→
∞
lim
a
k
d)
S
n
=
∑
k
=
0
n
a
k
S_n=\displaystyle\sum_{k=0}^{n} a_k
S
n
=
k
=
0
∑
n
a
k
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