Question

How do I write 5+7+9+11+13+15+17 in sigma notation?

Answer 1

What is the common factor that we are adding each time?

Answer 2

2

Answer 3

Right, so we're looking at something that looks like:
\[\sum Number + 2n\]

The "Number" will depend on where you want to start your summation. Usually, we begin from n = 0 or from n = 1. We'll need to make that choice now. Which would you like to do?

Answer 4

n=0

Answer 5

Alright, so if n = 0, and we want to get the number 5, what is our "Number?"

Answer 6

would it be 3?

Answer 7

Not 3

We want:
Number + 2*0 = 5

Answer 8

so, it would be 5? since 2*0=0

Answer 9

Yep :)

Answer 10

So, we now we just need to decide when to stop our summation. The last term that we want is 17. So, what is n when the result is 17?

5+2n = 17

Answer 11

6?

Answer 12

Yep :)

And we just put it all together:
\[\sum_{n=0}^{6}5+2n = 5+7+9+11+13+15+17\]

Answer 13

Thanks!

Answer 14

Does it all make sense?

Answer 15

yes

Answer 16

Outstanding :)