Purchase Solution

# Computing summations and integrals using indefinite summation

Not what you're looking for?

Given a summation of a function from, say, zero to N, one may consider analytically continuing the upper limit N to the set of reals or the complex plane. Consider such an analytic continuation for the summation 1 + 2 + 3 +...+N, without invoking the well known result of this summation. Argue that the summation is a second degree polynomial, find its zeros and determine the result this way. Repeat this for the summation of the squares 1^2 + 2^2 + 3^2 +...+N^2, by arguing on the basis that this should be a third degree polynomial.

Evaluate the integral from 0 to infinity of exp(-x^2)/(1+x^2)dx using Glaisher's theorem.

##### Solution Summary

The solution contains a general explanation on the indefinite summation method and Glaisher's method to compute integrals of even functions from 0 to infinity. Detailed solutions of the three problems are given.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Multiplying Complex Numbers

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

##### Probability Quiz

Some questions on probability

##### Graphs and Functions

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