Heuristics to highlight

Consider a simpler problem (smaller numbers); Use suitable numbers (instead of algebra); Make a systematic list; Look for patterns.

Simplify \[\frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + ... + \frac{1}{{100 \times 101}}\], leaving your answer in the simplest form in terms of n. Justify your answer.