Question

The population of a local species of beetle can v found using an infinite geometric series where a sub(1)=880 and the common ration is 1/4. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

Answer 1

@texaschic101

Answer 2

@SolomonZelman

Answer 3

the terms decrease geometrically to a smaller and smaller magnitude, so you CAN approximate the sum.

Answer 4

For \(\large\color{black}{ a_1=880}\) and \(\large\color{black}{ r=¼ }\)

Answer 5

Is the sum going to be divergent?

Answer 6

Well, I guess not, because we can approximate an answer...

Answer 7

You will have ∞ on top of the Σ.\(\huge\color{white}{ \rm │ }\)
AND the equation (next to Σ) will be something like \(\large\color{black}{880(¼)^n }\)
And index (below Σ) will be n=0 .\(\LARGE\color{white}{ \rm │ }\)

Answer 8

Can you write the sigma notation ?

Answer 9

there are thwo choices where you have n: either i, or i-1

Answer 10

What do you mean? write out the answer choices?

Answer 11

sigma with imaginary numbers? I can't really see why is that ...

Answer 12

on the bottom (the index) it says i=1, not n=0

Answer 13

That's on all of them

Answer 14

Why can't it be \[\Large \sum_{n=0}^{∞} ~880\left(\begin{matrix} \frac{1}{4} \end{matrix}\right)^n\]

Answer 15

I have no idea- that just not one of the answers...

Answer 16

Ohh i is for index, it is not an imaginary.

Answer 17

\[\Large \sum_{i=0}^{∞} ~880\left(\begin{matrix} \frac{1}{4} \end{matrix}\right)^i\]

Answer 18

That makes so much more sense!!

Answer 19

but putting an "i" instead of "n" is very confusing.

Answer 20

I never liked "i" as just a variable (that is not an imaginary)

Answer 21

It really is. maybe not in really early math, when you have no idea what an imaginary number is, but now that the imaginary is part of our mental math vocabulary, it shouldn't be used like that anymore.

Answer 22

yes

Answer 23

I hate when people solve equations with i and a bunch of other variables and say solve for x.... (I keep asking "is i an imaginary or...)

Answer 24

Do you have any more questions about your question ?

Answer 25

I know! It makes math even more confusing that it already is.

Answer 26

Should the exponent of the parentheses be i or i-1?

Answer 27

If the index is i=1

Answer 28

it is i-1 if you start from n=1, and it should be just i, if you start from n=0

Answer 29

Thank you! I'm just starting from i=1 because that's what the problem did. It doesn't make any sense to me.

Answer 30

It is either

\[\Large \sum_{i=0}^{∞} 880\left(\begin{matrix} \frac{1}{4}\end{matrix}\right)^i\]


or

\[\color{reblue}{ \Large \sum_{i=1}^{∞} 880\left(\begin{matrix} \frac{1}{4}\end{matrix}\right)^{i-1}}\]