Question

Let s(n) = (see equation). Find the limit of s(n) as n approaches infinity.

Answer 1

\[\sum_{i=1}^{n}(1 + 1/n)^2 (1/n)\]

Answer 2

I'm pretty sure that is not the correct sum.

Answer 3

the way you have it written the limit as n goes to infinity is 1

Answer 4

I'm sorry, it's 1 +i/n in the first part

Answer 5

write as an integral

Answer 6

you will get 7/3

Answer 7

how?

Answer 8

\[\int\limits_{a}^{b}f(x)dx=\lim_{n\to \infty}\sum_{i=1}^{n}f(a+i\Delta x)\Delta x\]

Answer 9

I'm sorry, I still don't' understand. Can you list the first few steps?

Answer 10

\[\lim_{n\to\infty}\sum_{i=1}^{n}\left(1 + \frac{i}{n}\right)^2 \frac{1}{n}\]

\[\lim_{n\to\infty}\sum_{i=1}^{n}\left(1 + i\frac{1}{n}\right)^2 \frac{1}{n}\]

\[\lim_{n\to\infty}\sum_{i=1}^{n}\left(1 + i\frac{2-1}{n}\right)^2 \frac{2-1}{n}\]

\[=\int\limits_{1}^{2}x^2dx\]

Answer 11

where is the 2 -1 coming from?

Answer 12

\[\Delta x=\frac{b-a}{n}\]

i know at a must be 1 so b must be 2 so that \[\frac{b-a}{n}=\frac{1}{n}\]