Chapter 7 of 10
Revision Notes
Some Special Sequences — Revision Notes
NIOS · Class 12 · Mathematics
Some Special Sequences revision notes for NIOS Class 12 Mathematics: 4 topics in quick points. Part of the NIOS Class 12 Mathematics syllabus.
45 questions25 flashcards6 formulas & key relations5 concepts
Interactive on Super Tutor
Studying Some Special Sequences? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.
Free trial, no card needed.
Super Tutor
Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Some Special Sequences.
Key Topics to Revise
1
What is a Series?
- A sequence is an ordered list of numbers following a definite rule, e.g., 1, 4, 9, 16, ...
- A series is formed by adding the terms of a sequence: 1 + 4 + 9 + 16 + ...
- Every sequence has a corresponding series associated with it.
2
The Three Master Formulas — Σn, Σn², Σn³
- These three formulas are the backbone of this entire chapter. Memorise them perfectly.
- Σn = sum of first n natural numbers = n(n+1)/2
- Σn² = sum of squares of first n natural numbers = n(n+1)(2n+1)/6
3
Finding Sum of Special Series — Step-by-Step Method
- The METHOD for ALL series sum problems is the same — always follow these 4 steps.
- STEP 1: Find tₙ — identify the nth term of the series by observing the pattern.
- STEP 2: Express tₙ as a polynomial in n — expand any products completely.
4
Proof of Standard Formulas Using Method of Differences
- The method of differences (telescoping) is used to DERIVE the standard sum formulas.
- For Σn²: Use the identity n³ - (n-1)³ = 3n² - 3n + 1. Write this for n = 1, 2, 3, ..., n and add.
- For Σn³: Use the identity n⁴ - (n-1)⁴ = 4n³ - 6n² + 4n - 1. Write this for n = 1, 2, ..., n and add.
Get complete notes with diagrams and examples
Full NotesKey Concepts
A series is an expressionThe nth termThe series 1 + 2 +The series 1² + 2² +The series 1³ + 2³ +
Frequently Asked Questions
What are the important topics in Some Special Sequences for NIOS Class 12 Mathematics?
Key topics in Some Special Sequences include What is a Series?, The Three Master Formulas — Σn, Σn², Σn³, Finding Sum of Special Series — Step-by-Step Method, Proof of Standard Formulas Using Method of Differences. Study these first, then practise questions on each for the NIOS Class 12 board exam.
How should I revise Some Special Sequences for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Some Special Sequences. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Some Special Sequences
For serious students
Get the full Some Special Sequences chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for NIOS Class 12 Mathematics. Free to start, no card needed.