Question

Use summation notation to express the sums.
a) 3 + 6 + 9 + 12 + 15
b) 2/5 + 3/7 + 4/9 + 5/11

Answer 1

Show us your best guess and we'll help show you how to fix it.

Answer 2

\[\sum_{i=3}^{15}2i-1\]
\[\sum_{i=2}^{5} \frac{ i }{ i+3}\]

Answer 3

Those don't give me the right answers though. They're really close, but no quite there.

Answer 4

So in the first one it might be nice to try to figure out what's changing each step? It looks like every next piece is just 3 more than the last one. So if you rewrite it as:

1*3+2*3+3*3+4*3+5*3

Maybe that makes it easier? Factor out the 3 and see which is the "counting" part.
\[\sum_{n=1}^{5}3*n\]

Answer 5

So you do not always have to necessarily start at the first given value? For example in part a, at 3?

Answer 6

Yeah you're doing pretty good, these can be kinda tricky at first but they're not so bad once you get used to them.

Well you don't have to start at or end at any place as long as you add up all the numbers you want. But usually there's a nice preference. For instance, I could have written:

\[\sum_{n=1}^{5}3*n=\sum_{k=4}^{8}3*(k-3)\] since they are going to give the exact same numbers, although the one on the left looks nicer.

Answer 7

Oh alright! That makes sense. I'm working on part b now.

Answer 8

For the second one I got
\[\sum_{i=1}^{5}\frac{ i+1 }{ 2i+3 }\]

Answer 9

You have the top part of the fraction correct, but you need to work on the bottom part.

A note to make, if you want even numbers you might want to play with:

2n

and if you want odd, well just add 1 to get

2n+1

So from there you can sort of play around a little, but those are fairly commonly used.

Answer 10

Does what I typed worked?

Answer 11

Nope. The first term is correct, but the second term is 3/6 instead of 3/7 so you need to count by odd numbers.

Answer 12

For the numerator I got 2(2), and for the denominator I got 2(2)+3 for the second term, which would give me 3/7 though.

Answer 13

I don't see what's wrong with rrachheaell's answer