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Explain why the convergence of a sequence depends only on the convergence of the tail of the sequence.

Short Answer

Expert verified

For any >0, there exists some N > 0 such that if k > N, ak-L<forkN.

By definition, only the terms determines the convergence of the sequence. And this refers to the tail of the sequence.

Step by step solution

01

Step 1. Given Information.

The convergence of the sequence.

02

Step 2. The definition.

For any >0, there exists some N > 0 such that if k > N, ak-L<forkN.

By definition, only the terms determines the convergence of the sequence. And this refers to the tail of the sequence.

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