Question

Find the limit of s(n) as n → ∞.
s(n) = (1/n^2)*[n(n + 1)/8]

Answer 1

is it

\(s(n) = (\dfrac{1}{n^2})\dfrac{n(n + 1)}{8}\)

??

if not, maybe draw it??

Answer 2

sorry, that is it

Answer 3

\[s(n) = \frac{ 1 }{ n^2 }\left[ \frac{ n(n+1) }{ 8} \right]\]

Answer 4

divide it out!

\[s(n) = \frac{ 1 }{ n^2 }\left[ \frac{ n^2+n }{ 8} \right]\]

\[s(n) =\left[ \frac{ 1+ \frac{1}{n} }{ 8} \right]\]

Answer 5

see it?

Answer 6

oh yeah...

Answer 7

so if \(n \to \infty\) , then get \(n\) underneath something so **the something** goes to zero......

Answer 8

um... so what is the final answer?

Answer 9

You may notice that IrishBoy divided each term by the largest value of n, n^2, getting another form of the same function. Now what is the limit as n approaches infinity of 1/n ?

Answer 10

zero?

Answer 11

Yes, so what must the limit be?

Answer 12

1/8

Answer 13

Right.

Answer 14

Thank you Daniel

Answer 15

np