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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.

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.

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#2

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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.

**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.

**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?).

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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

**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?).
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#4

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Y is equal to logbase2 x. x=y.

**iusama0**)Y is equal to logbase2 x. x=y.

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Can you make any progress now?

**Plücker**)Can you make any progress now?

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#6

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What is the solution, if geometric progression is 3 is not given?

**iusama0**)What is the solution, if geometric progression is 3 is not given?

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Have you done part one? Do you know the required formula?

**Plücker**)Have you done part one? Do you know the required formula?

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

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#8

(Original post by

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

**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

Anyway, you know the first term and the sum to infinity. Can you write an equation and solve it to find the common ratio?

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(Original post by

I thought that your common ratio was .

Anyway, you know the first term and the sum to infinity. Can you write an equation and solve it to find the common ratio?

**Plücker**)I thought that your common ratio was .

Anyway, you know the first term and the sum to infinity. Can you write an equation and solve it to find the common ratio?

equation is:

S = a/1-r

a = first term

r = common ratio

S = sum to infinity

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#10

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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

**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

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