RD Sharma Class 11 Solutions Chapter 21 - Some Special Series (Ex 21.2) Exercise 21.2 - Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 21 - Some Special Series (Ex 21.2) Exercise 21.2
1. Where can I find accurate, step-by-step solutions for RD Sharma Class 11 Maths Chapter 21, Exercise 21.2?
Vedantu provides detailed, step-by-step solutions for all problems in RD Sharma Class 11 Maths Chapter 21 (Some Special Series), Exercise 21.2. These solutions are meticulously prepared by expert teachers and are fully aligned with the CBSE syllabus for the 2025-26 academic year, ensuring you understand the correct methodology for every question.
2. What are the key formulas needed to solve problems in Exercise 21.2 of 'Some Special Series'?
To correctly solve the questions in Exercise 21.2, you must master the formulas for the sum of the first 'n' terms of these special series:
Sum of first n natural numbers (Σn) = n(n+1)/2
Sum of squares of first n natural numbers (Σn²) = n(n+1)(2n+1)/6
Sum of cubes of first n natural numbers (Σn³) = [n(n+1)/2]²
These are fundamental for finding the sum of any series where the nth term is a polynomial in 'n'.
3. Why is finding the nth term (Tₙ) the most crucial first step for problems in this exercise?
Finding the general or nth term (Tₙ) is the most critical first step because the sum of a series (Sₙ) is calculated as the summation of its nth term, i.e., Sₙ = ΣTₙ. Without a correct expression for Tₙ, you cannot apply the standard summation formulas (Σn, Σn², Σn³). This step effectively transforms a sequence of numbers into a solvable algebraic expression, forming the foundation for the entire solution.
4. How do you solve a question from Ex 21.2 where the series is given, but the nth term is not explicitly stated?
If a series like 1·2 + 2·3 + 3·4 + ... is given, your first task is to deduce the pattern to write its nth term (Tₙ). In this example, the nth term is clearly n(n+1), which expands to n² + n. Once you determine Tₙ, you find the sum Sₙ by calculating Σ(n² + n). Using summation properties, this becomes Σn² + Σn, and you can then substitute the standard formulas to find the final answer.
5. What are some common mistakes to avoid when solving problems from RD Sharma's Chapter 21, Exercise 21.2?
When solving problems from this exercise, students often make a few common errors. Be careful to avoid:
Incorrectly identifying the nth term: This is the most frequent error and will make the entire solution incorrect.
Algebraic calculation mistakes: The final simplification after applying formulas can be complex and prone to errors.
Applying formulas to the wrong series type: These special formulas are not for standard AP or GP series unless their nth term is expressed as a polynomial.
Forgetting summation properties: Failing to correctly split the summation, for example, Σ(Tₙ) = Σ(n² + n) = Σn² + Σn.
Vedantu's solutions show these steps clearly to help prevent such mistakes.
6. Can the formulas for Σn, Σn², and Σn³ be applied to any series?
No, these important formulas are exclusively for the sum of the first 'n' natural numbers, their squares, and their cubes. They cannot be directly used for general Arithmetic Progressions (APs) or Geometric Progressions (GPs). The core method in Chapter 21 is to express the nth term of a given series as a polynomial function of 'n', which then allows you to break it down into components that can be summed using these specific formulas.
7. How do the Vedantu solutions for Exercise 21.2 help in preparing for Class 11 final exams?
Our solutions for Exercise 21.2 are designed to teach the systematic problem-solving method required in Class 11 exams. Each solution logically explains the steps—from identifying the nth term to applying the correct summation formulas and simplifying the result. This methodical approach, aligned with the 2025-26 CBSE guidelines, helps build a strong conceptual foundation, which is key to scoring well in subjective examinations.
