Purchase Solution

Series Calculation and Its Convergent Properity

Not what you're looking for?

Ask Custom Question

(a) (i) Fine the sum of the integers from 17 to 92 inclusive.
(ii) Hence find the value of:

92
∑ (5+6i)
i = 17

(b) For each of the sequences below, decide whether it converges, and if it does, state its limit.

(i) a*subscript*n = 7 + 2(0.4)^n / 8(0.3)^n - 8 (n = 1, 2, 3, ... )

(ii) b *subscript* n = 3 - 9n^2 / 5n + 6 (n = 1, 2, 3, ... )

(c) Find the fraction equivalent to the infinite decimal: 0.638 163 816 381

Purchase this Solution
Solution Summary

The solution gives detailed steps on finding the sum of integer series and determining the convergent properties of some certain series. Also, a transformation between infinite decimal and fraction is computed step by step.

Solution Preview

Question 1

(a)
(i) Find the sum of the integers from 17 to 92 inclusive.

We have (92-17)+1=76 numbers. So the sum is (17+92)*76/2=4142

(ii) Hence find the value of

Using the result in part a, sum is ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Gregory's Series : Taylor Expansion, Interval of Convergence and Calculation of 'pi'

    So is the series . Now, we need to look at two endpoints x=-1 and x=1. For x=-1, becomes which is an alternating series and convergent. For x=1, becomes which is an alternating series and convergent.

  • 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.

  • Sequences & series

    c.Suppose that an is convergent and find its limit 3.Suppose that the partial sum of the series�. is given by �� Find a)b)c) 4.Determine whether series coverges or not.

  • the Cauchy condensation test

    Show that if a series is conditionally convergent, then the series obtained by its positive terms is divergent, and the series obtained by its negative terms is divergent. 3. give an example of a convergent series sum(a_n) such that sum(a_n^2) is not

  • convergent or divergent

    The solution determines whether the series is convergent or divergent by expressing the partial sum as a telescoping sum. If it is convergent, find its sum.

  • convergence or divergence

    Hence the series ∑▒b_n is not convergent. a_n sin⁡n Clearly and . Hence the series ∑▒b_n is convergent. a_n/((1+|a_n |)) Clearly . Hence the series ∑▒b_n is convergent.

  • Methods of Real Analysis by Richard Goldberg.

    = Since for each n and x, the denominator of the rational expression is always less than its numerator, the series converges uniformly. where denotes the partial sum of the series.

  • Convergence and Divergence of Series

    Hence the given series is convergent. We have . Hence we have . And the series is convergent. Hence the given series is convergent. 5 / ( a, c, d, f) We have Consider the series . We have .

  • Complex Sequences and Series: Convergence or Divergence?

    Because e^z is an entire function and its expansion sum(n from 0 to oo) (z^n)/n! converges for any z. 2. Diverge 3. Convergent and absolutely convergent. Because the series sum(n from 1 to infinity) z^n converges if and only if |z|<1.

View More Related Solutions