Why Students Fail at Telescoping Series (and How to Fix It)

Telescoping series is one of those techniques where students either see it instantly or never see it at all.

The universal pattern to look for:

If you can write the general term as f(n+1) - f(n) for some function f, the series telescopes.

That is the entire principle. Everything else is practice.

Most JEE students do not reach 30 telescoping problems. That is why they fail at them.