RD Sharma Solutions for Class 11 Maths Chapter 21 - Free PDF Download
RD Sharma Class 11 Some Special Series, cover the sums of the first ‘n’ natural numbers, squares of first ‘n’ natural numbers, and cubes of the first ‘n’ natural numbers. Students can refer to the RD Sharma Solutions For Class 11 Maths Chapter 21 PDF to get a clear idea of the concept of the special series. The solutions are prepared by our expert faculty team in a comprehensive manner to make it interesting for students to solve. These Solutions are available in PDF format on Vedantu and can be downloaded for free of cost.
Concepts covered in this chapter are the sum to ‘n’ terms of some other special series viz. series of natural numbers, series of the square of natural numbers, series of cubes of natural numbers, etc. RD Sharma Solutions are designed for CBSE students, according to the latest syllabus prescribed by the CBSE Board. Our expert teacher has designed these solutions in an easily understandable language. To practice is an essential task to learn and score well in Mathematics. The pdfs of RD Sharma Solutions For Class 11 Maths Chapter 21 are provided here. Students are advised to go through RD Sharma Solutions thoroughly before the final exams to score well in the exam.
Important Topics in RD Sharma Class 11 Math Chapter 21 Solutions.
The sum up to ‘n’ terms of some other special series is the main concept explained in this chapter. RD Sharma Solutions are designed for the students as per the latest syllabus and guidelines provided by CBSE. Methods of difference and summation of some special series are the other topics which are also covered here. Students are advised to thoroughly solve the textbook problems before the final exams and increase their abilities to solve complex problems.
Following are the Concepts Discussed in this Chapter.
Sum up to ‘n’ terms of some special series.
How to find the sum of first ‘n’ natural numbers.
How to find the sum of the squares of first ‘n’ natural numbers.
How to find the sum of the cubes of first ‘n’ natural numbers.
Method of difference.
Summation of some special series.
Exercises in RD Sharma Solutions For Class 11 Math Chapter 21
Exercise Wise Discussion of RD Sharma Solutions for Class 11 Math Chapter 21
Chapter 21, that is, some special series of Class 11 RD Sharma contains two exercises for the students that cover questions on all the topics discussed in the chapter.
There are a total of 12 questions in the first exercise, that is, exercise 21.1 that deal with questions related to the sum of the series.
In these questions, the students are provided with a series and they have to find the sum of the series by applying the formula.
The questions included in exercise 21.1 are a bit lengthy and require the students to pay good attention at each step.
The second exercise, that is, exercise 21.2 contains some special series that require the students to choose an apt technique for finding the successive difference in the given series and also calculating the formula of summation of series.
Questions related to arithmetic progression and geometric progression are also included in exercise 21.2.
The student must possess good knowledge on which formula to apply in a specific question, so as to gain good marks. Such questions appear really frequently in question papers.
There is an additional exercise provided in RD Sharma Solutions for Class 11 Math Chapter 21, that is, 21-VSAQ. This exercise provides the student with the most frequently asked questions that are designed by the experts so that the students can practice such questions.
This special exercise contains only 6 questions which are really helpful for the students and can fetch them with certain brownie points.
Tips for Class 11 Chapter 21 - Some Special Series
There are certain tips that each student should keep in mind if he or she wants to perform well in their exams like:
Students must practice as many questions as possible so that they are well versed with the solutions.
All students must revise their concepts on a daily basis so that they are clear with their concepts during the examination.
Every student must make a chapter wise list of all the formulas present in a chapter so that they can revise all formulas just before the exam.
Students must go through previous years question papers before their final examinations so that they have an idea about the pattern of question paper. Also, many times questions get repeated so students who have gone through previous year question papers will have an upper hand.
All students must solve sample papers as well. These sample papers act as a question bank for students and they get an idea of probable questions that may come in the exam on a particular topic.
Students must attempt all questions present in RD Sharma as well as this will help them in building their basics.
Why Should Students Refer to RD Sharma Math Solution Class 11 Chapter 21-Some Special Series?
There are various advantages provided by RD Sharma:
Students can practice different types of questions of various difficulty levels from a single book.
In case students face any doubt while solving problems, they can immediately refer to the RD Sharma Math Solution, so as to clear all their difficulties.
These solutions are given by our expert team, where we have included different ways of answering the question. Students can refer to the different kinds of solutions, students can get to understand the different ways of answering questions and arrange a suitable way which they find easy.
Solving the solution also benefits the students to help them in the learning process in an easy way.
All the exercise questions are covered in the RD Sharma Class 11 Math Chapter 21 Solutions. It helps students to revise the complete chapter and score good marks in the exams. Solutions prepared by Vedantu experts help students to understand the concepts in an easier way. Students get to know all the concepts in detail as the solutions provided by us are easy and reliable. RD Sharma Math Solutions for Class 11 Chapter 21 Some Special Series help students learn how to solve the various sums covered in this chapter, in a step-by-step manner.
FAQs on RD Sharma Class 11 Maths Solutions Chapter 21 - Some Special Series
1. What is the formula for the sum of the square of first N natural numbers?
Natural numbers represent the set of all whole numbers except 0. The calculation of the sum of the square of the first n natural number is easy if you know the formula for its calculation. The formula is universal and can be applied for any value of n. Therefore, each student must remember this formula so that they are able to solve questions easily. The sum of the square of the first N natural number can be calculated using the following formula:
( n(n+1)(2n+1) /6)
2. What is an AGP series?
The Arithmetic-Geometric Progression (AGP) is a sequence of which each term can be expressed as the product of an arithmetic progression and a geometric progression. The arithmetic-geometric series, commonly known as AGP, are formed by multiplying the corresponding terms of an arithmetic progression and geometric progression. The general form of an AGP is:
a, (a+d)r, (a+2d)r2, (a+3d)r3, (a+4d)r4, ……….. (a+(n-1)d)rn-1
Here, ‘a’ is the first term, ‘d’ is a common difference and ‘r’ is the common ratio.
3. How can we determine the nth term of an arithmetic sequence?
Arithmetic sequences are easy to determine. If you are provided with the common difference and first term in the question, you can simply put the values in the formula and determine the required term. Given an arithmetic sequence with the first term a1 and the common difference d, then the nth (or general) term is determined by an=a1+(n-1)d. Students should practice questions related to this concept as these types of questions often appear in exams and are highly scoring.
4. How will I benefit from RD Sharma Solutions for Class 11 Math Chapter 21?
RD Sharma Solutions for Class 11 Chapter 21, that is, some special series provided by Vedantu are very helpful for the students. These solutions will help students in preparing better for the exams. The step by step explanation provided by the team of experts at Vedantu will solve all the possible doubts that may arise in a student's mind. Moreover, all the formulae related to the chapter are also mentioned along with the solutions which will help students revise the formulae every now and then.
5. Can I get access to RD Sharma Solutions for Class 11 Math Chapter 21 while I am offline?
RD Sharma Solutions for Class 11 Math Chapter 21 are available in the form of a PDF file on the official website of Vedantu. The students can download the PDF file from the official website absolutely free of cost after registering through their mail id. Once the students have downloaded the PDF file on their system, they can view the solutions whenever and wherever they want without the requirement of any internet connection. This ensures that there is no hurdle between a student and his education.