Series | Proof That the Harmonic Series Diverges

Series | Proof That the Harmonic Series Diverges

Assessment

Interactive Video

Science, Mathematics

University

Hard

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The video tutorial introduces the harmonic series, explaining its definition and historical context, including a proof of its divergence by Nicole Oresme. The instructor provides a detailed proof of divergence, comparing the harmonic series with a smaller series to demonstrate its divergence. The general form of the series is discussed, highlighting that any constant over n results in divergence. The video concludes with applications of the harmonic series, emphasizing its use in the direct comparison test.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Who was the first to prove the divergence of the harmonic series?

Nicole Oresme

Leonhard Euler

Isaac Newton

Carl Gauss

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the basic form of the harmonic series?

1 + 2 + 3 + 4 + ...

1 + 1/4 + 1/9 + 1/16 + ...

1 + 1/2 + 1/3 + 1/4 + ...

1 + 1/3 + 1/5 + 1/7 + ...

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How are the terms grouped in the proof of the harmonic series' divergence?

In groups of five

In groups of ten

In groups of two, four, eight, etc.

In groups of three

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the second series used in the comparison smaller than the harmonic series?

It converges

It starts with a smaller number

Its terms are either equal or smaller

It has fewer terms

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the harmonic series when multiplied by a constant?

It becomes finite

It becomes zero

It converges

It remains divergent

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of the harmonic series in mathematical tests?

It is used to calculate limits

It is used to prove convergence

It is used in probability theory

It is used in the direct comparison test

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the condition for the constant in the general form of the harmonic series?

It must be less than one

It must be an integer

It can be any number

It must be positive