# RD Sharma solutions for Class 11 Mathematics Textbook chapter 21 - Some special series [Latest edition]

## Chapter 21: Some special series

Exercise 21.1Exercise 21.2Exercise 21.3Exercise 21.4
Exercise 21.1 [Page 10]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 21 Some special series Exercise 21.1 [Page 10]

Exercise 21.1 | Q 1 | Page 10

1+ 3+ 53 + 73 + ...

Exercise 21.1 | Q 2 | Page 10

22 + 42 + 62 + 82 + ...

Exercise 21.1 | Q 3 | Page 10

1.2.5 + 2.3.6 + 3.4.7 + ...

Exercise 21.1 | Q 4 | Page 10

1.2.4 + 2.3.7 +3.4.10 + ...

Exercise 21.1 | Q 5 | Page 10

1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ...

Exercise 21.1 | Q 6 | Page 10

1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...

Exercise 21.1 | Q 7 | Page 10

3 × 12 + 5 ×22 + 7 × 32 + ...

Exercise 21.1 | Q 8.1 | Page 10

Find the sum of the series whose nth term is:

2n2 − 3n + 5

Exercise 21.1 | Q 8.2 | Page 10

Find the sum of the series whose nth term is:

2n3 + 3n2 − 1

Exercise 21.1 | Q 8.3 | Page 10

Find the sum of the series whose nth term is:

n3 − 3n

Exercise 21.1 | Q 8.4 | Page 10

Find the sum of the series whose nth term is:

n (n + 1) (n + 4)

Exercise 21.1 | Q 8.5 | Page 10

Find the sum of the series whose nth term is:

(2n − 1)2

Exercise 21.1 | Q 9 | Page 10

Find the 20th term and the sum of 20 terms of the series 2 × 4 + 4 × 6 + 6 × 8 + ...

Exercise 21.2 [Page 18]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 21 Some special series Exercise 21.2 [Page 18]

Exercise 21.2 | Q 1 | Page 18

3 + 5 + 9 + 15 + 23 + ...

Exercise 21.2 | Q 2 | Page 18

2 + 5 + 10 + 17 + 26 + ...

Exercise 21.2 | Q 3 | Page 18

1 + 3 + 7 + 13 + 21 + ...

Exercise 21.2 | Q 4 | Page 18

3 + 7 + 14 + 24 + 37 + ...

Exercise 21.2 | Q 5 | Page 18

1 + 3 + 6 + 10 + 15 + ...

Exercise 21.2 | Q 6 | Page 18

1 + 4 + 13 + 40 + 121 + ...

Exercise 21.2 | Q 7 | Page 18

4 + 6 + 9 + 13 + 18 + ...

Exercise 21.2 | Q 8 | Page 18

2 + 4 + 7 + 11 + 16 + ...

Exercise 21.2 | Q 9 | Page 18

$\frac{1}{1 . 4} + \frac{1}{4 . 7} + \frac{1}{7 . 10} + . . .$

Exercise 21.2 | Q 10 | Page 18

$\frac{1}{1 . 6} + \frac{1}{6 . 11} + \frac{1}{11 . 14} + \frac{1}{14 . 19} + . . . + \frac{1}{(5n - 4) (5n + 1)}$

Exercise 21.3 [Pages 18 - 19]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 21 Some special series Exercise 21.3 [Pages 18 - 19]

Exercise 21.3 | Q 1 | Page 18

Write the sum of the series 2 + 4 + 6 + 8 + ... + 2n.

Exercise 21.3 | Q 2 | Page 18

Write the sum of the series 12 − 22 + 32 − 42 + 52 − 62 + ... + (2n − 1)2 − (2n)2.

Exercise 21.3 | Q 3 | Page 19

Write the sum to n terms of a series whose rth term is r + 2r.

Exercise 21.3 | Q 4 | Page 19

If $\sum^n_{r = 1} r = 55, \text{ find } \sum^n_{r = 1} r^3$ .

Exercise 21.3 | Q 5 | Page 19

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.

Exercise 21.3 | Q 6 | Page 19

Write the sum of 20 terms of the series $1 + \frac{1}{2}(1 + 2) + \frac{1}{3}(1 + 2 + 3) + . . . .$

Exercise 21.3 | Q 7 | Page 19

Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...

Exercise 21.3 | Q 8 | Page 19

Let Sn denote the sum of the cubes of first n natural numbers and sn denote the sum of first n natural numbers. Then, write the value of $\sum^n_{r = 1} \frac{S_r}{s_r}$ .

Exercise 21.4 [Pages 19 - 20]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 21 Some special series Exercise 21.4 [Pages 19 - 20]

Exercise 21.4 | Q 1 | Page 19

The sum to n terms of the series $\frac{1}{\sqrt{1} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{7}} + . . . . + . . . .$  is

• $\sqrt{2n + 1}$

• $\frac{1}{2}\sqrt{2n + 1}$

• $\sqrt{2n + 1} - 1$

• $\frac{1}{2}\left\{ \sqrt{2n + 1} - 1 \right\}$

Exercise 21.4 | Q 2 | Page 19

The sum of the series

$\frac{1}{\log_2 4} + \frac{1}{\log_4 4} + \frac{1}{\log_8 4} + . . . . + \frac{1}{\log_2^n 4}$ is

• $\frac{n (n + 1)}{2}$

• $\frac{n (n + 1) (2n + 1)}{12}$

• $\frac{n (n + 1)}{4}$

• none of these

Exercise 21.4 | Q 3 | Page 19

The value of  $\sum^n_{r = 1} \left\{ (2r - 1) a + \frac{1}{b^r} \right\}$ is equal to

• $a n^2 + \frac{b^{n - 1} - 1}{b^{n - 1} (b - 1)}$

• $a n^2 + \frac{b^n - 1}{b^n (b - 1)}$

• $a n^3 + \frac{b^{n - 1} - 1}{b^n (b - 1)}$

• none of these

Exercise 21.4 | Q 4 | Page 19

If ∑ n = 210, then ∑ n2 =

•  2870

• 2160

• 2970

• none of these

Exercise 21.4 | Q 5 | Page 19

If Sn = $\sum^n_{r = 1} \frac{1 + 2 + 2^2 + . . . \text { Sum to r terms }}{2^r}$, then Sn is equal to

• 2n − n − 1

•   $1 - \frac{1}{2^n}$

• $n - 1 + \frac{1}{2^n}$

• 2n − 1

Exercise 21.4 | Q 6 | Page 20

If $1 + \frac{1 + 2}{2} + \frac{1 + 2 + 3}{3} + . . . .$ to n terms is S, then S is equal to

• $\frac{n (n + 3)}{4}$

• $\frac{n (n + 2)}{4}$

• $\frac{n (n + 1) (n + 2)}{6}$

•  n2

Exercise 21.4 | Q 7 | Page 20

Sum of n terms of the series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} +$ .......  is

• $\frac{n (n + 1)}{2}$

• 2n (n + 1)

• $\frac{n (n + 1)}{\sqrt{2}}$

• 1

Exercise 21.4 | Q 8 | Page 20

The sum of 10 terms of the series $\sqrt{2} + \sqrt{6} + \sqrt{18} +$ .... is

• $121 (\sqrt{6} + \sqrt{2})$

• $243 (\sqrt{3} + 1)$

• $\frac{121}{\sqrt{3} - 1}$

• $242 (\sqrt{3} - 1)$

Exercise 21.4 | Q 9 | Page 20

The sum of the series 12 + 32 + 52 + ... to n terms is

• $\frac{n (n + 1) (2n + 1)}{2}$

• $\frac{n (2n - 1) (2n + 1)}{3}$

• $\frac{(n - 1 )^2 (2n + 1)}{6}$

• $\frac{(2n + 1 )^3}{3}$

Exercise 21.4 | Q 10 | Page 20

The sum of the series $\frac{2}{3} + \frac{8}{9} + \frac{26}{27} + \frac{80}{81} +$ to n terms is

• $n - \frac{1}{2}( 3^{- n} - 1)$

• $n - \frac{1}{2}(1 - 3^{- n} )$

• $n + \frac{1}{2}( 3^n - 1)$

• $n - \frac{1}{2}( 3^n - 1)$

## Chapter 21: Some special series

Exercise 21.1Exercise 21.2Exercise 21.3Exercise 21.4

## RD Sharma solutions for Class 11 Mathematics Textbook chapter 21 - Some special series

RD Sharma solutions for Class 11 Mathematics Textbook chapter 21 (Some special series) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics Textbook chapter 21 Some special series are Sum to N Terms of Special Series, Introduction of Sequence and Series, Concept of Sequences, Concept of Series, Arithmetic Progression (A.P.), Geometric Progression (G. P.), Relationship Between A.M. and G.M..

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