Is my summation notation correct?

1. Jan 14, 2013

Lo.Lee.Ta.

It has been a while since I've had to figure out summation notation.
Would you please look through my solutions, and tell me if they're correct?
Thank you so much! :)
1a.

6
Ʃ 1/6 = ?
i=1

1/6 + 1/6 + 1/6 + 1/6 + 1/6 +1/6 = 6/6 = 1

What makes me doubt my answer is that it seems like the i=1 was for nothing...

If the summation was for i/6, though, would this be correct?

(1/6) + (2/6) + (3/6) + (4/6) + (5/6) + (6/6) = 21/6 = 7/2

And if the summation were written like this:

6
Ʃ i/6 = ?
i=3

Would this be correct? (3/6) + (4/6) + (5/6) + (6/6) = 18/6 = 3

1b.

10
Ʃ 1/10 = ?
i=1

(1/10)*10 = 10/10 = 1

1c.

100
Ʃ 1/100 = (1/100)*100 = 100/100 = 1
i=1

2. Jan 14, 2013

Dick

Looks fine to me.

3. Jan 14, 2013

Lo.Lee.Ta.

Oh, okay. Thank you! :)

4. Jan 14, 2013

Staff: Mentor

No, it serves a purpose. The index i doesn't explicitly appear in each term, but i = 1 gives the starting value of the index, and 6 gives the ending value. That says that there are 6 terms in the summation (6 - 1 + 1).

In this summation $\sum_{n = 3}^{25} n^2$, there are 25 - 3 + 1 = 23 terms.