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From Wikipedia, the free encyclopedia
f
n
(
k
)
=
{
1
,
if
k
=
n
0
,
if
k
≠
n
{\displaystyle f_{n}(k)={\begin{cases}1,&{\text{if }}k=n\\0,&{\text{if }}k\neq n\end{cases}}}
f
(
k
)
=
lim
n
→
∞
f
n
(
k
)
=
0
{\displaystyle f(k)=\lim _{n\to \infty }f_{n}(k)=0}
a
n
=
∑
i
=
1
∞
f
n
(
i
)
=
1
{\displaystyle a_{n}=\sum _{i=1}^{\infty }f_{n}(i)=1}
lim
n
→
∞
∑
i
=
1
∞
f
n
(
i
)
=
lim
n
→
∞
a
n
=
1
{\displaystyle \lim _{n\to \infty }\sum _{i=1}^{\infty }f_{n}(i)=\lim _{n\to \infty }a_{n}=1}
∑
i
=
1
∞
lim
n
→
∞
f
n
(
i
)
=
∑
i
=
1
∞
f
(
i
)
=
0
{\displaystyle \sum _{i=1}^{\infty }\lim _{n\to \infty }f_{n}(i)=\sum _{i=1}^{\infty }f(i)=0}
From Wikipedia, the free encyclopedia
f
n
(
k
)
=
{
1
,
if
k
=
n
0
,
if
k
≠
n
{\displaystyle f_{n}(k)={\begin{cases}1,&{\text{if }}k=n\\0,&{\text{if }}k\neq n\end{cases}}}
f
(
k
)
=
lim
n
→
∞
f
n
(
k
)
=
0
{\displaystyle f(k)=\lim _{n\to \infty }f_{n}(k)=0}
a
n
=
∑
i
=
1
∞
f
n
(
i
)
=
1
{\displaystyle a_{n}=\sum _{i=1}^{\infty }f_{n}(i)=1}
lim
n
→
∞
∑
i
=
1
∞
f
n
(
i
)
=
lim
n
→
∞
a
n
=
1
{\displaystyle \lim _{n\to \infty }\sum _{i=1}^{\infty }f_{n}(i)=\lim _{n\to \infty }a_{n}=1}
∑
i
=
1
∞
lim
n
→
∞
f
n
(
i
)
=
∑
i
=
1
∞
f
(
i
)
=
0
{\displaystyle \sum _{i=1}^{\infty }\lim _{n\to \infty }f_{n}(i)=\sum _{i=1}^{\infty }f(i)=0}
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