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# RD Sharma Class 11 Chapter 21 Solutions (Some Special Series)

RD Sharma Solutions for Class 11 Maths Chapter 21 ‘Some Special Series’ are made to help you prepare for the central board of state examinations.  These RD Sharma Solutions are not only referred by CBSE students but students from other state boards, such as ICSE, AP Board, UP Board and those appearing in competitive examinations like JEE Mains, JEE advanced.

RD Sharma Class 11 Maths Chapter 21 includes 22 questions divided into 2 exercises for your practice. It has also added exercise 21 VSAQ (Very-Short-Answer-Type-Questions) for the detailed explanation of the chapter. It allows you to understand the core concept of series by giving you the solutions for the most frequently asked questions. This chapter also involves a mixture of AP and GP series questions.

RD Sharma Class 11 Solutions for Chapter 21 ‘Some Special Series’ are very helpful as they include clear explanations and are available online. They provide comprehensive knowledge to the subject by enabling you to attempt all the questions in the examination irrespective of its difficulty level.

## Topics covered in RD Sharma Solutions for Class 11 Maths Chapter 21 – Some Special Series

This topic includes a special series. It may also be a series related to arithmetic or geometric progression. Special series are those which are special or put in some special sequence. For example, if you go to a clothing shop to buy a shirt of L, M size and there are different colours for the same sizes available, put in the good sequence of L  and M size order, then it would be easy for you to take a shirt and try. The same is the case with some special sequence of series. The sequences may be limited or unlimited.

Some special types of series are discussed here are:

1.           Total of Ist natural numbers up to n digits (1+2+3+4+5+6+7+8+9+…. Till n)
2.           Total of squares of First natural numbers up to n digits ( 12 + 22 +3…. ++ till n2)

III.            Total of cubes of First natural numbers up to n digits (1  +23  ++…. ++ till n 3 )

1.           Total of series of some special cases.
•     Here we know the formula to find the First natural numbers  with the help of AP

= N (N+1)/2

Depending upon the given series of squares or cubes or sum of digits,

The formula applies.

For example:

• Sum of natural numbers  12 + 22 +32, s this series is not given in AP or GP terms then it will first be directed in AP or GP terms ;

Let  a3 – (a-1)3 = 3a2 – 3a +1

If we take the value of (a) as, a = 1, 2, 3 and so on.  (a) is also supposed to be n here

•      Sum of Cubes of the First Natural Numbers up to n digits  (1 + 2 + 3 +… + n)

Here we use the formula,

(a+1)4 – a4 = 4a3 + 6a2 + 4a + 1

We will take the values of a= 1 and solve it, then it will be taken as a= 2 and so on, putting the values of all the digits into the given formula.

•    Sum of series: the infinite limit of any sum of series starting from 1 is the sum of all the given First n digits.

### Discussion on the Exercises of RD Sharma Solutions for Class 11 Chapter 21

• In exercise 21.1, there are 12 questions given about the sum of the series. The various series are given and by applying the formula, you have to find out the sum of the series.
• These questions are a bit lengthy in nature and time consuming as they involve calculations based on a formula. So every step requires good attention.
• In exercise 21.2, some special series is given, which shows the choosing of the apt technique of finding the successive difference given in the series and then applying the formula of summation of series.
• The AP and GP series of questions are also asked in this exercise. It requires a good hand on AP and GP chapters. Proper knowledge of the right application of formula will help you gain good marks. These types of questions are very frequent in the question paper.
• In the last exercise 21-VSAQ, it is an additional exercise given for the practice of the most frequently asked questions specially designed by the experts. There are only 6 questions in this exercise which are marks fetching in nature.

### Benefits of RD Sharma Solutions for Class 11 chapter 21 by Instasolv

RD Sharma Class 11 Maths Solutions Chapter 21 are designed according to the current syllabus of CBSE to help in increasing your aptitude skills. You should consider taking help from these solutions before preparing for final exams. Instasolv is benefiting all students at no cost. You can find all the solutions online for RD Sharma Class 11 Maths Solutions Chapter 21. This will help you manage your time by understanding the logic behind the questions and solving them without losing your marks. The questions are given following the RD Sharma exercises.

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