# Homework Help: Limit of summation notation

1. Mar 27, 2012

### Biosyn

1. The problem statement, all variables and given/known data

http://desmond.imageshack.us/Himg100/scaled.php?server=100&filename=img20120327195119.jpg&res=medium [Broken]

2. Relevant equations

3. The attempt at a solution

I just plugged in ∞ for n

[2+$\frac{3}{∞}$]2 ($\frac{3}{∞}$) =

[2+0]2 (0) = 0

Did I do the problem correctly? I might need a refresher on summation notations.

Here are the multiple choice answers:

a. 0
b. 1
c. 4
d. 39
e. 125

Last edited by a moderator: May 5, 2017
2. Mar 27, 2012

### 4570562

Seems right to me.

3. Mar 27, 2012

### Dick

It's not right at all. You can't plug n=infinity into that. It looks like a Riemann sum approximation to an integral to me. None of the multiple choice answers that you've shown are correct either.

4. Mar 27, 2012

### Biosyn

I couldn't fit all of the choices into the frame.

The choices:

a. 0
b. 1
c. 4
d. 39
e. 125

5. Mar 27, 2012

### Dick

I'm not going to pick an answer for you. Show me how to get it. Put x=k/n and express that as a limiting sum for a Riemann integral over x.

6. Mar 27, 2012

### Biosyn

Okay , I think I did it.

(3/n) = ΔX
ΔX = (b-a)/n

so, b=3 ; a=0

xi = a + [i(b-a)]/n

xi = [0 + (3k)/n + 2]2

f(xi) = (x+2)2

The integral would be $^{3}_{0}$∫(x+2)2

7. Mar 28, 2012

### Ray Vickson

One of the listed answers is correct.

RGV

8. Mar 28, 2012

Right.