Adding a chain of unit fractions

Let \(n\) be a positive integer.

1. Show that \(\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{1}{n(n+1)}\).[2]
2. Hence find the exact value of \(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\cdots+\dfrac{1}{99\times100}\).[3]
3. Find the least number of terms of this pattern, starting from \(\dfrac{1}{1\times2}\), whose sum exceeds \(0.99\).[2]