FP1 OCR - Converging series help please!

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.