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Calculus, all content (2017 edition)

Course: Calculus, all content (2017 edition) > Unit 7

Lesson 9: Comparison tests

Direct comparison test
Worked example: direct comparison test
Direct comparison test
Limit comparison test
Worked example: limit comparison test
Limit comparison test
Proof: harmonic series diverges

Direct comparison test

We know that

0, is less than, start fraction, 1, divided by, n, cubed, plus, 1, end fraction, is less than, start fraction, 1, divided by, n, cubed, end fraction

for any n, is greater than or equal to, 1.

Considering this fact, what does the direct comparison test say about sum, start subscript, n, equals, 1, end subscript, start superscript, infinity, end superscript, space, start fraction, 1, divided by, n, cubed, plus, 1, end fraction ?

Stuck?

Calculus, all content (2017 edition)

Course: Calculus, all content (2017 edition) > Unit 7

Problem