# Evaluate the limit

## Homework Statement

lim.......... (1 + 1/n^2)(7/n+1)
n->infinity

## The Attempt at a Solution

lim.......... (1 + 1/n^2)(7/n+1)
n->infinity

= (7/n + 1) + (7/n^3 + n^2)

bring out 7 because constant..

7lim.......... (1/n + 1) + (1/n^3 + n^2)
n->infinity
.
.
.
.
.
7lim.......... (n^2 + n + 1) / (n^3 + 2n^2 +n)
n->infinity

limit does not exist.. am i correct?

## The Attempt at a Solution

Related Calculus and Beyond Homework Help News on Phys.org
Before you try to mathematically rearrange anything, try imagining what happens to (1+(1/n^2)) as n approaches infinity. Then do the same with (7/(n+1)). What do you see?

Mark44
Mentor

## Homework Statement

lim.......... (1 + 1/n^2)(7/n+1)
n->infinity

## The Attempt at a Solution

lim.......... (1 + 1/n^2)(7/n+1)
n->infinity

= (7/n + 1) + (7/n^3 + n^2)

bring out 7 because constant..

7lim.......... (1/n + 1) + (1/n^3 + n^2)
n->infinity
.
.
.
.
.
7lim.......... (n^2 + n + 1) / (n^3 + 2n^2 +n)
n->infinity

limit does not exist.. am i correct?
No. Don't multiply the two factors. Each one has a limit that is readily obtainable. As n gets large without bound, what happens to 1/n2? What happens to 1 + 1/n2? What happens to 7/n? What happens to 7/n + 1?

The limit does exist.