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Mathematics
Quick fact
The integral test shows that the harmonic series 1 + 1/2 + 1/3 + ... diverges because its related integral diverges, while the p-series with p=2 converges.
Why this is interesting
You know how some sums, like 1 + 1/2 + 1/3 + ..., seem to keep growing forever, but others, like 1 + 1/4 + 1/9 + ..., approach a finite number? The integral test gives a clever way to tell which is which using the idea of area under a curve.
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Subjects · study & training · careers
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