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How do you determine if a sequence converges or diverges?

Find the limit as n approaches infinity. 2. If the limit exists and is finite, it converges. 3. If the limit does not exist or is infinite, it diverges.

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How do you determine if a sequence converges or diverges?

Find the limit as n approaches infinity. 2. If the limit exists and is finite, it converges. 3. If the limit does not exist or is infinite, it diverges.

How to find partial sums $s_1, s_2, s_3$ of a series?

Calculate $a_1, a_2, a_3$ . 2. $s_1 = a_1$ . 3. $s_2 = a_1 + a_2$ . 4. $s_3 = a_1 + a_2 + a_3$ .

What does the Sequence Convergence Theorem state?

If a sequence is both bounded and monotonic, then the sequence converges.

Explain the concept of convergence for a sequence.

A sequence converges if its limit as n approaches infinity exists and is a finite number. It approaches a specific value.

Explain the concept of divergence for a sequence.

A sequence diverges if its limit as n approaches infinity does not exist (oscillates) or is infinite. It does not approach a specific value.

Explain the difference between a sequence and a series.

A sequence is a list of numbers, while a series is the sum of the numbers in a sequence.

What does it mean for a series to converge?

The sum of the infinite terms approaches a finite value.

What does it mean for a series to diverge?

The sum of the infinite terms does not approach a finite value; it either goes to infinity or oscillates.