Question

Find the 9th partial sum of the summation of 3i-4, from i equals 1 to infinity.

I think I know how to do it but I can't tell if it's arithmetic or geometric so I know which formula to use.

Answer 1

You could try breaking this into 2 separate summations.

Let the first one be the sum (i=1 to i=9) of 3i. This would be the same as

"three times the sum from i=1 to i=9 of i alone."

The other sum would be simple to find: 9 times 4. Don't forget to put a - sign in front of this sum.

Answer 2

What is the sum of \[\sum_{1}^{9}i~?\]

Answer 3

There's a formula for that. although I don't recall it at the moment.

what is the sum of i when i goes from 1 to 1? It's just 1.
what is the sum when i goes from 1 to 2? It's 3.

Go ahead and experiment. Have fun. Show all work.

Answer 4

Would it just be 9 for that part then? I'm not quite sure how to do it with the i

Answer 5

I ranges from 1 to 9, and we're adding them up. What do you get?

The 2nd partial sum would be 1+2=3; the 3rd would be 1+2+3=6, and so on.

Answer 6

OKay, so then it would be 1+2+3+4+5+6+7+8+9 which would be 45 right?

Answer 7

To me, if you jot down some numbers , you can see what is going on
Like this: if i =1, then the first number is 3*1 -4 =-1
if i =2, then the second number is 3*2 -4 = 2
do some more, you can see it is a arithmetic series, and it is easy

Answer 8

Okay, so then because it's an arithmetic series, we have to use \[\frac{ n }{ 2 }(a _{1}-a_{9})\]

Answer 9

we have another formula for it

Answer 10

Reverse the order. a9 - a1.

Answer 11

Why would it be the other way around?

Answer 12

or you can use it but have to find a9 first

Answer 13

4.5(-1+23)
which would be 99

Answer 14

Technically both ways would work I guess; if you had a9 and then a1

Answer 15

Because the i values increase. if y ou were to subtract 9 from 1, you'd get -8. It's unlikely that that negative number would lead you to the correct sum.

You're free to use whichever approach you want. I'd recommend you separate the addends and create 2 summations: 3 times the summation from 1 to 9 of i, and then subtract the summation from 1 to 9 of 4.

Answer 16

summation is by definition addition (or combination, if both pos. and neg numbers are involved). That alone suggests that you have an arith. sequence here, not a geom sequence. Geom sequences involve multiplication and exponentiation.

Answer 17

Alright, so then would the answer I got be correct?

Answer 18

yup

Answer 19

Alright, thanks. I'm also kind of having trouble with another question, if you have time to spare at all.