How to Solve 1/(√1+√2) + 1/(√2+√3) + … + 1/(√99+√100) | Rationalization Trick | Telescoping series

How to Solve 1/(√1+√2) + 1/(√2+√3) + … + 1/(√99+√100) | Rationalization Trick | Telescoping Series

In this video, we solve a classic and tricky math problem step by step:
1/(√1+√2) + 1/(√2+√3) + … + 1/(√99+√100) = ?
🔑 Key concept used: Rationalization of the denominator using conjugate surds — a powerful trick that turns each term into a telescoping series, making the whole sum collapse beautifully to just √100 − √1 = 10 − 1 = 9.
✅ What you'll learn:
How to rationalize irrational denominators with conjugate surds
The telescoping series technique
How to simplify complex summations in seconds
📚 Perfect for: Class 9 / Class 10 students, GCSE Maths, competitive exam prep (Olympiad, SAT, AMC), and anyone learning surds and rationalization.
⏱️ Answer: 9 — Watch to see why!

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Видео How to Solve 1/(√1+√2) + 1/(√2+√3) + … + 1/(√99+√100) | Rationalization Trick | Telescoping series канала Ashutosh Maurya