Best unit 8 mathematical induction binomial theorem solved notes class 11 punjab boards – 100% solved exercises with easy step-by-step solutions, graphs, diagrams & marking scheme from new book (PECTAA, Punjab Curriculum and Textbook Board, Ali Brothers, Ilmi Kitab Khana, Scholar Publications, Caravan Book House, Farhan Publishers).Perfect for Punjab boards exams 2026 – score 90+ marks!
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Exercise 8.1 – Proofs by Induction (All Questions Solved) Exercise 8.1 Page 211 Full Solutions ↳ Exercise 8.1 Complete Solved PDF ↳ Q1(i) log x^n = n log x Proved ↳ Q1(ii) Sum (3n-1) = n/2 (3n+1) Proved ↳ Q1(iv) Sum 2*3^{n-1} = 3^n -1 Proved ↳ Q1(v) Sum n(2n+1) = n(n+1)(4n+5)/6 Proved ↳ Q1(vi) Sum 1/n(n+1) = 1 -1/(n+1) Proved ↳ Q1(vii) r + r² + … + r^n = r(1-r^n)/(1-r) Proved
All Remaining Exercises + Review Exercise (100% Solved) ↳ Exercise 8.2 Binomial Theorem ↳ Exercise 8.3 Expansions & Coefficients ↳ Exercise 8.4 Applications ↳ Review Exercise Unit 8 Full Solved
Bonus Resources ↳ Induction Binomial Formulas Cheat Sheet PDF ↳ Top 30 Proof & Expansion Shortcuts ↳ Induction Binomial Video Series ↳ Unit 8 Past Papers Solved (2018-2025) ↳ Unit 7 Permutations Combinations Notes ↳ Unit 9 Division Polynomials Coming Soon
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External Links
- PCTB Official → pctb.punjab.gov.pk
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