If $$ \left\langle a_{n}\right\rangle $$ and $$ \left\langle b_{n}\right\rangle $$ are two sequences such that $$ \lim _{n \rightarrow \infty} a_{n}=i, \lim _{n \rightarrow \infty} b_{n}=m $$, then prove that: $$ \lim _{n \rightarrow \infty}\left(a_{n}+b_{n}\right)=l+m $$

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Peters Wells · Accepted Answer

If the limits of two sequences $$ a_n $$ and $$ b_n $$ as $$ n $$ approaches infinity are $$ i $$ and $$ m $$ respectively, then the limit of their sum $$ a_n + b_n $$ is $$ i + m $$.

If \( \left\langle a_{n}\right\rangle \) and \( \left\langle b_{n}\right\rangle \) are two sequences such that \( \lim _{n \rightarrow \infty} a_{n}=i, \lim _{n \rightarrow \infty} b_{n}=m \), then prove that: \( \lim _{n \rightarrow \infty}\left(a_{n}+b_{n}\right)=l+m \)

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If \( \left\langle a_{n}\right\rangle \) and \( \left\langle b_{n}\right\rangle \) are two sequences such that \( \lim _{n \rightarrow \infty} a_{n}=i, \lim _{n \rightarrow \infty} b_{n}=m \), then prove that: \( \lim _{n \rightarrow \infty}\left(a_{n}+b_{n}\right)=l+m \)

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