(a) Why does the sequence of real numbers fn(x1) necessarily contain a convergent subsequence (fnk )? To indicate that the subsequence of functions (fnk ) is generated by considering the values of the functions at x1, we will use the notation fnk = f1,k.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.