# Prove direct from definition

1. May 19, 2009

### asset101

let an = $$\frac{(2n+1)}{(3n+7)}$$. Prove direct from definition that an$$\rightarrow2/3$$.

Any help would be appreciated.
Cheers

2. May 19, 2009

### tiny-tim

ok … first step in a question like this is …

what is the definition of the statement "lim((2n+ 1)/(3n+7)) = 2/3"?

3. May 19, 2009

### AUMathTutor

Here's an idea... as long as n isn't zero, the following two things are the same:

(2n+1)/(3n+7) = [(2n)(1+1/2n)]/[(3n)(1+7/3n)]

What happens as the n's get bigger and bigger to the terms 1/2n and 7/3n?

4. May 19, 2009

### HallsofIvy

Staff Emeritus
That's the simplest way of finding the limit but it doesn't "prove from the definition".

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