Nice Fraction Math Simplification | Telescoping Series Trick | Find the Value

Nice Fraction Math Simplification | Telescoping Series Trick | Find the Value 1/(1x2) + 1/(2x3) + ... + 1/(9x10) = ? Learn the telescoping series trick: split every term, cancel the middle, keep the ends. Full step-by-step solution, three verifications, bonus examples (gap of 2, reverse trick, sum to infinity) and common mistakes. IN THIS VIDEO: The splitting identity 1/(n(n+1)) = 1/n - 1/(n+1), proved The great cancellation: why only the ends survive Verification by direct addition AND by decimals General formula n/(n+1), bonus sums up to 1/(19x20), gap-of-2 sums 4 common mistakes + speed drill CHAPTERS: 0:00 Intro — The Monster Problem 0:44 Why the Direct Way Hurts 1:23 Meet All Nine Terms 2:05 Step 1 — Look at ONE Term 2:36 Step 2 — The Splitting Identity (Proved) 3:14 Step 3 — Term 2 Splits Too 3:48 Step 4 — Term 3 Splits Too 4:22 Split the Rest — Terms 4 to 9 4:58 Warm-up — Just 2 Terms 5:35 Verify the Warm-up 6:05 Warm-up — 3, 4, 5 Terms 6:48 The Full Sum — Split EVERY Term 7:26 The Chain in Full 8:01 The Great Cancellation 8:34 Brackets Keep the Signs Honest 9:05 The Answer — 9/10 9:35 Why Not 10/11? — The Off-by-One Trap 10:12 Why 'Telescoping'? 10:49 VERIFICATION — The Slow Way (1) 11:30 VERIFICATION — The Slow Way (2) 12:06 Decimal Check — Climbing to 0.9 12:45 The General Formula 13:21 Worked Example — Up to 1/(14x15) 14:08 Common Mistake 1 — The Broken Split 14:46 Common Mistake 2 — Cancelling the Ends 15:21 Common Mistake 3 — Plus Instead of Minus 15:55 Common Mistake 4 — Cancelling Strangers 16:30 BONUS 1 — Up to 1/(19x20) 17:05 BONUS 2 — Start in the Middle 17:44 Verify Bonus 2 the Slow Way 18:22 BONUS 3 — A Gap of 2 19:01 Bonus 3 — Finish It 19:43 Verify Bonus 3 the Slow Way 20:21 What If the Numerator Is Not 1? 20:56 The REVERSE Trick — Find n 21:32 To Infinity and Beyond 22:11 Same Trick with Squares — Odd Numbers 22:49 How to SPOT Telescoping in an Exam 23:30 Recap — The 4 Moves 24:05 SPEED DRILL 24:38 Answer + Your Turn COMMENT QUESTION: 1/(2x3) + 1/(3x4) + ... + 1/(99x100) = ? (Hint: first survivor 1/2, last survivor 1/100.) Write your answer in the comments! About Darkhan Mentor: Step-by-step lessons, explained slowly and clearly, so every student can follow. Every rule comes with examples, every answer is verified. #DarkhanMentor #EnglishGrammar #Maths