User:Gmalivuk

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f_{n}(k)={\begin{cases}1,&{\text{if }}k=n\\0,&{\text{if }}k\neq n\end{cases}}

f(k)=\lim _{n\to \infty }f_{n}(k)=0

a_{n}=\sum _{i=1}^{\infty }f_{n}(i)=1

\lim _{n\to \infty }\sum _{i=1}^{\infty }f_{n}(i)=\lim _{n\to \infty }a_{n}=1

\sum _{i=1}^{\infty }\lim _{n\to \infty }f_{n}(i)=\sum _{i=1}^{\infty }f(i)=0

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