FP1 OCR - Converging series help please! Watch

hiya123
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Report Thread starter 4 years ago
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Hiya,
so I understand when a fraction 'tends to 0' when its the sum to infinity but I don't get when it tends to 1?

Because 1/n tends to 0, but n/(n+1) tends to 1, but for both, the top of the fraction is smaller than the bottom?
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Smaug123
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(Original post by hiya123)
Hiya,
so I understand when a fraction 'tends to 0' when its the sum to infinity but I don't get when it tends to 1?
Does it tend to 0 when the top of the fraction is smaller than the top, like 1/n and tends to 1 when the top is bigger than the bottom, like n/(n+1)?
I'm confused by your first statement.

The second statement: \frac{n}{n+1} \to 1. This is because \frac{n}{n+1} = 1-\frac{1}{n+1}, and I'm sure you'll agree that \frac{1}{n+1} \to 0.

In general, you get convergence to 0 when the denominator grows substantially faster than the numerator. For instance, \frac{n}{n^2} \to 0 because n^2 gets bigger faster than n does.
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hiya123
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(Original post by Smaug123)
I'm confused by your first statement.

The second statement: \frac{n}{n+1} \to 1. This is because \frac{n}{n+1} = 1-\frac{1}{n+1}, and I'm sure you'll agree that \frac{1}{n+1} \to 0.

In general, you get convergence to 0 when the denominator grows substantially faster than the numerator. For instance, \frac{n}{n^2} \to 0 because n^2 gets bigger faster than n does.
Sorry I realised after it made no sense!

Thanks so much I get it now!
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