# Tutor.com Infinite Series, Taylor Series Session

##### Apr. 12, 2012

Session Transcript - Math - Calculus, 4/3/2012 8:42PM - Tutor.comSession Date: 4/3/2012 8:42PM
Length: 13.6 minute(s)
Subject: Math - Calculus

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Patron (Customer)
[00:00:00] Consider the following recursively defined sequence: Find the value of a2002. Give a clear explanation of how you obtained your answer.

System Message
[00:00:00] *** The student has 179 minutes remaining. ***

Marjorie P (Tutor)
[00:00:12] Hi! Welcome to tutor.com .

Patron (Customer)
[00:00:32] Hello

Marjorie P (Tutor)
[00:00:44] Hi there.

Patron (Customer)
[00:01:25] I started this problem and so far I have solved for a3, a4, and a5

Marjorie P (Tutor)
[00:01:35] Awesome. What did you get?

Patron (Customer)
[00:01:54] but i got 0,-1,1

Marjorie P (Tutor)
[00:02:21] Great.
[00:02:47] Do you have any ideas how to find the 2002 element?

Patron (Customer)
[00:03:47] i tried to think about it, like doing the an=a1+(n-1)(d) formula, but I dont know

Marjorie P (Tutor)
[00:04:24] This sequence follows a pattern. If you try 3 more elements, you'll see that it repeats.
[00:04:42] Can you find the next 3?

Patron (Customer)
[00:05:05] 0,-1,1

Marjorie P (Tutor)
[00:05:39] Good job. It will keep repeating in that pattern.

Patron (Customer)
[00:05:54] 2002 times?!

Marjorie P (Tutor)
[00:06:25] Well, on to infinity, really. But if you can figure out a formula for the pattern, you can calculate any element.
[00:07:05] a3 and a6=0. And that will be true for a9, a12, a15...
[00:07:17] Every 3rd element is zero.
[00:07:36] So if you look at the subscript n, and it's divisible by 3, that element is zero.
[00:08:08] Do you see what I mean?

Patron (Customer)
[00:08:24] i see

Marjorie P (Tutor)
[00:08:41] Is 2002 divisible by 3?

Patron (Customer)
[00:08:49] no

Marjorie P (Tutor)
[00:09:03] Okay. What's the remainder?

Patron (Customer)
[00:09:35] 667.33333

Marjorie P (Tutor)
[00:10:29] The remainder is 1. 2001 is divisible by 3, but 2002 is one more than that.
[00:11:10] Looking at the pattern on the board, can you figure out what a2002 is?

Patron (Customer)
[00:11:22] -1?

Marjorie P (Tutor)
[00:11:28] That's it!

Patron (Customer)
[00:12:40] Oh, I understand now. That made a lot of sense! Thank you!

Marjorie P (Tutor)
[00:12:51] You're so welcome! Are we all set?

Patron (Customer)
[00:13:19] Yup! thank you again and have a great night!