Question 1.

1. Homework Statement

State whether the limit exists for (Limit as x aproaches infinity ==> (n+1)/(n+1)

and give the value of it if it does exist. Graph the first 5 terms of each sequence.

3. The Attempt at a Solution

if you use any number for "n", numerator divided by denominator would equal 1.

Question 2:

1. Homework Statement
The sequence a1, a2, a3 ..... has the following possible nth terms. For the case given below try various large values for n and guess the limit. Confirm that guess by manipulating the general term an.

a(n) = (n+1) / (n^2+1)

I'm taking a intro Calc class, so this is probably easy stuff for you guys, that's why I lumped both questions into one thread. Anhow, I'm not looking for an answer since it's in my book, I just want to know what the question is asking for.

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and.... where's that thread that explains how to use syntax.

edit: nm, I just found it....latex not syntax lol

Dick
Homework Helper
So what's your question? Did you follow the suggestion and substitute various values of n? What's your guess of the limit?

question 1: limit equals 1?

question 2:

an = n + 1 / n^2 + 1

possible answers: 11/101, 101/10001, 1001/1000001 appears to have limit of zero?

but how does it have limit of zero?

Dick
Homework Helper
Yep. Can you prove it? Divide numerator and denominator by n.

Dick
Homework Helper
question 2:

an = n + 1 / n^2 + 1

possible answers: 11/101, 101/10001, 1001/1000001 appears to have limit of zero?

but how does it have limit of zero?
Same answer, yes. Can you prove it? Divide numerator and denominator by n^2.

oh wait....question 2's answer is from the book, not mine.

I attempted it the same way..............except

what I don't understand is how it has a limit of zero?

Dick
Homework Helper
Ok, divide numerator and denominator of 2) by n^2. This gives you (1/n+1/n^2)/(1+1/n^2), right? What's the limit of 1/n and 1/n^2?

wait....

the question is (n + 1) / (n^2 +1)

so divide num/denom by n^2 it should be

(n/n^2) + (1/n^2) / (n^2/n^2) + (1/n^2) right?

then it goes

(1/n) + (1/n^2) / 1 + (1/n^2)

then it goes, which is the step I don't understand...

(0+0) / (1 + 0) = 0/1 = 0

where are all these zero's coming from?

Dick