iusama0
Badges: 4
Rep:
?
#1
Report Thread starter 2 months ago
#1
A geometric progression has first term logbase2 27 and common difference logbase2 x.

i) Find the set of values of y for which the geometric progression has a sum to infinity.
ii) Find the exact value of y for which the sum to infinity of the geometric progression is 3.
0
reply
Plücker
Badges: 14
Rep:
?
#2
Report 2 months ago
#2
(Original post by iusama0)
A geometric progression has first term logbase2 27 and common difference logbase2 x.

i) Find the set of values of y for which the geometric progression has a sum to infinity.
ii) Find the exact value of y for which the sum to infinity of the geometric progression is 3.
Do you have notes or a textbook? If so read the relevant section if not Google it. In particular, what is the requirement on the common ratio in order for there to be a sum to infinity? For part ii, if necessary, remind yourself of the formula for the sum to infinity and then form an equation and solve it to find y (or is it x?).
0
reply
iusama0
Badges: 4
Rep:
?
#3
Report Thread starter 2 months ago
#3
(Original post by Plücker)
Do you have notes or a textbook? If so read the relevant section if not Google it. In particular, what is the requirement on the common ratio in order for there to be a sum to infinity? For part ii, if necessary, remind yourself of the formula for the sum to infinity and then form an equation and solve it to find y (or is it x?).
Y is equal to logbase2 x. x=y.
1
reply
Plücker
Badges: 14
Rep:
?
#4
Report 2 months ago
#4
(Original post by iusama0)
Y is equal to logbase2 x. x=y.
Can you make any progress now?
0
reply
iusama0
Badges: 4
Rep:
?
#5
Report Thread starter 2 months ago
#5
(Original post by Plücker)
Can you make any progress now?
What is the solution, if geometric progression is 3 is not given?
0
reply
Plücker
Badges: 14
Rep:
?
#6
Report 2 months ago
#6
(Original post by iusama0)
What is the solution, if geometric progression is 3 is not given?
Have you done part one? Do you know the required formula?
0
reply
iusama0
Badges: 4
Rep:
?
#7
Report Thread starter 2 months ago
#7
(Original post by Plücker)
Have you done part one? Do you know the required formula?
Yes!
If the geometric progression has a sum to infinity, the common ratio, r must be less than 1 and more than -1, so -1<r<1 and r=log2(y) so -1<log2(y)<1

log2(y)>-1 is same as 2^(-1)<y i.e. 1/2<y

log2(y)<1 is the same as 2^1>y i.e. 2>y

So y must be in between 1/2 and 2 i.e. 1/2<y<2
0
reply
Plücker
Badges: 14
Rep:
?
#8
Report 2 months ago
#8
(Original post by iusama0)
Yes!
If the geometric progression has a sum to infinity, the common ratio, r must be less than 1 and more than -1, so -1<r<1 and r=log2(y) so -1<log2(y)<1

log2(y)>-1 is same as 2^(-1)<y i.e. 1/2<y

log2(y)<1 is the same as 2^1>y i.e. 2>y

So y must be in between 1/2 and 2 i.e. 1/2<y<2
I thought that your common ratio was \log_2 x.

Anyway, you know the first term and the sum to infinity. Can you write an equation and solve it to find the common ratio?
0
reply
iusama0
Badges: 4
Rep:
?
#9
Report Thread starter 2 months ago
#9
(Original post by Plücker)
I thought that your common ratio was \log_2 x.

Anyway, you know the first term and the sum to infinity. Can you write an equation and solve it to find the common ratio?
first term is logbase2 27 and sum to infinity are unknow.
equation is:
S = a/1-r
a = first term
r = common ratio
S = sum to infinity
0
reply
Plücker
Badges: 14
Rep:
?
#10
Report 2 months ago
#10
(Original post by iusama0)
first term is logbase2 27 and sum to infinity are unknow.
equation is:
S = a/1-r
a = first term
r = common ratio
S = sum to infinity
S = 3.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (26)
18.06%
I'm not sure (3)
2.08%
No, I'm going to stick it out for now (50)
34.72%
I have already dropped out (3)
2.08%
I'm not a current university student (62)
43.06%

Watched Threads

View All