- #1

- 12

- 0

We need to solve the following problem:

∞ r-1

find x if ∑ (3x/2) = 4

r=1

We know the answer is 1/2, but we have no idea how they got that answer. Can anyone help?

Thanks,

Sammie

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter sammieh
- Start date

- #1

- 12

- 0

We need to solve the following problem:

∞ r-1

find x if ∑ (3x/2) = 4

r=1

We know the answer is 1/2, but we have no idea how they got that answer. Can anyone help?

Thanks,

Sammie

- #2

- 12

- 0

I hope this makes sense to someone!

- #3

0rthodontist

Science Advisor

- 1,230

- 0

Do you know the formula for an infinite geometric sum?

- #4

- 12

- 0

Sn = u1(r^n – 1)

---------- where Sn is really S sub n and u1 is really u sub 1?

r-1

- #5

0rthodontist

Science Advisor

- 1,230

- 0

What does that formula mean? Identify u1, r, and especially n.

- #6

- 12

- 0

r is the constant common ratio and u1 is the first term of the series and I think n is a term in the series??

- #7

0rthodontist

Science Advisor

- 1,230

- 0

Well, first step is to find out what n is. You have to know what your formulas mean before you'll be able to use them.

You might also have another formula that is more directly useful, but you should still understand that one.

You might also have another formula that is more directly useful, but you should still understand that one.

Last edited:

- #8

- 12

- 0

o.k. n is the number of terms we are adding up. In our case infinity???

Right?

Right?

- #9

0rthodontist

Science Advisor

- 1,230

- 0

Then it's just a matter of applying the formula to the series you gave and solving for x.

- #10

- 12

- 0

u1/r-1 ?

and is the limit 1 as r goes to infinity?

- #11

0rthodontist

Science Advisor

- 1,230

- 0

- #12

- 12

- 0

and if r^n goes to 1 then wouldn't r^n-1 go to 0?

- #13

0rthodontist

Science Advisor

- 1,230

- 0

Pick some r < 1 and find out what it does. What is r^10? What is r^20?

- #14

- 12

- 0

- #15

0rthodontist

Science Advisor

- 1,230

- 0

Well, does it?

- #16

- 12

- 0

yes it does. as we increased the exponent the answer kept getting closer and closer to 1.

- #17

0rthodontist

Science Advisor

- 1,230

- 0

What's 0.5^2?

- #18

- 12

- 0

.5 ^ 2 = .25

- #19

0rthodontist

Science Advisor

- 1,230

- 0

Now you may be able to find that limit.

- #20

- 12

- 0

Sn = 4, u1=1 and r=3x/2, so

4 = 1/(1-3x/2)

solve for x and x = 1/2!

FINALLY!

- #21

0rthodontist

Science Advisor

- 1,230

- 0

Yep, that's right.

- #22

- 12

- 0

thanks for your help!

Share: