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###### Geometric sequence

Original post by mqb2766

If your sequence is 2, 4, 8, ...? Then the common ratio is ...

If not, can you upload the original question.

If not, can you upload the original question.

I’m just confused about what they did to get this for the sum

Original post by mqb2766

Its a famous sum, but the series is

2 + 4 + 8 + 16 + ... + 2^16

So the common ratio for the successive terms is ...? The obvious answer is the correct one.

2 + 4 + 8 + 16 + ... + 2^16

So the common ratio for the successive terms is ...? The obvious answer is the correct one.

2? But does the common ratio not have to be between |x|<1 or it that only for sum to infinity? Also why is the 1 negative?

Original post by Bigflakes

2? But does the common ratio not have to be between |x|<1 or it that only for sum to infinity? Also why is the 1 negative?

* Yes, r=2.

* The |r|<1 condition is only for a sum to infinity as you say, as you want the sum to converge to a finite value, so the terms in the series must decay (exponentially/geometrically). When the series has a finite number of terms, you just use the (easy to derive) expression.

* When you say the 1 negative, do you mean on the numerator / denominator? If so, you can multiply the usual expression by -1/-1 (so multiply both the numerator and denominator by -1). Then both of the expressions are positve for this series.

(edited 1 year ago)

Original post by mqb2766

* Yes, r=2.

* The |r|<1 condition is only for a sum to infinity as you say, as you want the sum to converge to a finite value, so the terms in the series must decay (exponentially/geometrically). When the series has a finite number of terms, you just use the (easy to derive) expression.

* When you say the 1 negative, do you mean on the numerator / denominator? If so, you can multiply the usual expression by -1/-1 (so multiply both the numerator and denominator by -1). Then both of the expressions are positve for this series.

* The |r|<1 condition is only for a sum to infinity as you say, as you want the sum to converge to a finite value, so the terms in the series must decay (exponentially/geometrically). When the series has a finite number of terms, you just use the (easy to derive) expression.

* When you say the 1 negative, do you mean on the numerator / denominator? If so, you can multiply the usual expression by -1/-1 (so multiply both the numerator and denominator by -1). Then both of the expressions are positve for this series.

Ohh so it doesn't matter if I use the other version?

Original post by Bigflakes

Ohh so it doesn't matter if I use the other version?

Its a fraction, you can multiply numerator and denominator by anything (well non-zero and has to be same multiplier top and bottom).

Original post by mqb2766

Its a fraction, you can multiply numerator and denominator by anything (well non-zero and has to be same multiplier top and bottom).

Thank you

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