Prove that the sums and differences of convergent sequences are convergent

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- Mar 2nd 2008, 02:00 PMnatesterConvergent Sequence proof
Prove that the sums and differences of convergent sequences are convergent

- Mar 2nd 2008, 02:07 PMPlato
This is the trick to the proof.

$\displaystyle \left| {\left( {a + b} \right) - \left( {a_n + b_n } \right)} \right| = \left| {\left( {a - a_n } \right) + \left( {b - b_n } \right)} \right| \le \left| {\left( {a - a_n } \right)} \right| + \left| {\left( {b - b_n } \right)} \right|

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