# Limit as n approaches infinity

## Homework Statement

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

(1 + 3n-1)/3n

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Dick
Homework Helper

## Homework Statement

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

(1 + 3n-1)/3n
You are supposed to show an attempt to solve it. Try it. Break it into two fractions.

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

Dick
Homework Helper
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?
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?

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?
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?

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

Yes. But you didn't need to plug numbers in. 3^n=3^(n-1)*3. So 3^(n-1)/3^n=1/3.
so it the answer is zero?

1/3 x 0

HallsofIvy
Homework Helper
Where did you get that "0" you are multiplying?

Where did you get that "0" you are multiplying?
the limit as x approaches infinity of 1/3n

Dick