Comparison test Definition and 106 Threads

Homework Statement Does xn converge (Sum from n=1 to infinity) of xn = 1/(n + SQRTn) Homework Equations Using comparision test The Attempt at a Solution I separted into fractions of 1/SQRTn - 1/(1 + SQRTn) and i know that both of these diverge since the power of n is less than...

Homework Statement First questions is: How to choose between using the ordinary comparison test, or using the limit comparison test? Homework Equations The Attempt at a Solution then, for these two problems below, i decide to use the limit comparison test: SUM n_infinity...

Homework Statement heres the equations: http://img407.imageshack.us/img407/738/untitledzk8.jpg there are two equations, a and b. Homework Equations 3/n^2 for a, and 1/n for b. The Attempt at a Solution Using the limit comparison test, i don't understand why to use 3/n^2...

Hi, I've been thinking about the comparison test for integrals. Usually when I have an integrand where the denominator is f(x) + something positive I can usually find a suitable bound without much trouble. However when the denomoninator of the integrand is f(x) - something positive finding a...

I'm supposed to compare the series \sum_{n=0}^{\infty}\frac{1}{n!} to some other series to see if the one above converges or diverges. I have no idea of what to compare it to. I know by the ratio test that the above series converges, that is if I'm doing the ratio test correctly...

Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is...