\(\Rightarrow\text{What's your favourite programme?}\)

\(A=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{99.100}\)

\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(A=\dfrac{1}{2}-\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{1}{4}-\dfrac{1}{4}\right)-\left(\dfrac{1}{5}-\dfrac{1}{5}\right)-...-\left(\dfrac{1}{99}-\dfrac{1}{99}\right)-\dfrac{1}{100}\)

\(A=\dfrac{1}{2}-0-0-0-...-0-\dfrac{1}{100}\)

\(A=\dfrac{1}{2}-\dfrac{1}{100}\)

\(A=\dfrac{50}{100}-\dfrac{1}{100}\)

\(A=\dfrac{49}{100}\)