5.12 Integral test

Integral test

Lessons

Notes:
Note *The integral test states the following:
If f(x)=anf(x)=a_n and f(x)f(x) is a continuous, positive decreasing function from [i,][i,\infty], then we can say that:
1. If if(x)dx\int_{i}^{\infty}f(x)dx is convergent, then the series n=ian\sum_{n=i}^{\infty}a_n is also convergent.
2. If if(x)dx\int_{i}^{\infty}f(x)dx is divergent, then the series n=ian\sum_{n=i}^{\infty}a_n is also divergent.
  • 2.
    P Series versus Integral test
    Use the integral test instead of the p-series test to show that the series converge or diverge.
  • 3.
    Convergence/Divergence of Integral Test
    Determine whether the following series converge or diverge using the integral test.
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Integral test

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