Integral and series

Related BrainMass Solutions

• Divergence and Convergence

  241875 Divergence and Convergence ** Please see the attached file for the complete problem description ** Please show all work (see attached) 1) Use integral test to determine if a series converges or diverges.

• Integral Test for Convergence

  Also, we know it is a geometric series with |r|=1/e<1, so we know that converges. The Integral Test for Convergence is investigated. The geometric series in integrals are provided.

• Limits : Summation Series

  Therefore, we can write the integral test: The improper integral is convergent if and only if series is convergent.

• Integral test of series

  This shows how to use the integral test to see if a series converges or diverges.

• Integral test: Convergence or divergence of a series.

  So by integral test we know the series (1) is not convergent. The integral test is used to determine the convergence or divergence of a series.

• Convergent or divergent series

  Use the integral test to determine if the series converges or diverges Solution: The integral is convergent and so the series must also be convergent by the Integral Test. 6.

• Series converges

  By the integral test, the series converges for p>1 by comparison with integral(x^(-p), x=1..infinity). The series diverges for 0< p <=1 when using the same comparison and integral.

• Singularities, Convergence of Taylor Series, Residues and Contour Integral

  170579 Singularities, Convergence of Taylor Series, Residues and Contour Integral Consider the complex function: f(z) = 1/(z^2 + z + 1)(z + 5i) a) Find and classify the singularities of f(z); b) Without finding the series explicitly, determine

• Convergent or divergent series

  Use the integral test to determine if the series converges or diverges Solution: The integral is convergent and so the series must also be convergent by the Integral Test. 5.