You are here:

# Calculus/Series

Question

Consider the sequence a_n = ((-1)^n)/(sqrt(n))

(a) List the first 10 terms of this sequence (starting with n = 1) and plot them as points on a graph.

(b) Find a number A such that |a_n|< (1/5)  for all n > A.

(c) What is the limit as n approaches infinity of a_n

(a) can't really be done, but here are the terms:
1   -1
2   0.707106781
3   -0.577350269
4   0.5
5   -0.447213595
6   0.40824829
7   -0.377964473
8   0.353553391
9   -0.333333333
10   0.316227766

(b) For the term |a_n| to be less than 1/5, since we have a squareroot involved,
that would mean n would have to be greater than 5^2, so n > 25 would work.

(c) The limit is 0 since there is an n term in the denominator.

Calculus

Volunteer

#### Scotto

##### Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).

##### Experience

Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.