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Chapter 2: Q5P (page 57)

Test each of the following series for convergence.

∑1n2+in

Short Answer

Expert verified

The series is divergent.

Step by step solution

01

Given Information

The series is ∑1n2+in.

02

Definition of the Convergent series

A series is said to be convergent if the terms of a series get close to zero when the number of terms moves towards infinity.

03

Test the convergence.

The series is ∑1n2+in=∑1n2+∑in..

The given series is the sum of convergent and divergent series hence the series is divergent.

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Most popular questions from this chapter

Solve for all possible values of the real numbers xand yin the following equations.

x+iy=3i-ix

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find x,y,r,θ in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

-1.

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findx,y,r,θ in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

5(cos20°+isin20°).

Test each of the following series for convergence.

∑1/(1+i)n

Question:First simplify each of the following numbers to the x+iyform or to thereiθform. Then plot the number in the complex plane.

(1.7-3.2i)2 .
See all solutions

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