Limit as n approaches infinity

1. Apr 14, 2013

KTiaam

1. The problem statement, all variables and given/known data

What is the limit of the given equations as n approaches infinity?

(1 + 3n-1)/3n

2. Apr 14, 2013

Dick

You are supposed to show an attempt to solve it. Try it. Break it into two fractions.

3. Apr 14, 2013

KTiaam

lim 1/3n + lim 3n-1/3n
n→∞ n→∞

the second equation:

you can cancel the 3n-1
and the second equations turns out to be the same as the first so that equals:

lim 1/3n
n→∞

so in approaches e?

4. Apr 14, 2013

Dick

e? No, what does 1/3^n approach? Just think about it. And 3^(n-1)/3^n isn't the same as the first term. What is it?

5. Apr 14, 2013

KTiaam

1/3n approaches 1/ a really big number.
1 over a big number equals 0.

(3n-1)/(3n)

you get

31/32

32/33

33/34

they all equal 1/3

so 1/3?

6. Apr 14, 2013

Dick

Yes. But you didn't need to plug numbers in. 3^n=3^(n-1)*3. So 3^(n-1)/3^n=1/3.

7. Apr 14, 2013

KTiaam

so it the answer is zero?

1/3 x 0

8. Apr 14, 2013

HallsofIvy

Staff Emeritus
Where did you get that "0" you are multiplying?

9. Apr 14, 2013

KTiaam

the limit as x approaches infinity of 1/3n

10. Apr 14, 2013

Dick

It's 0+1/3, isn't it?