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

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## Chapter 21: Some special series

Ex. 21.1Ex. 21.2Others

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

Ex. 21.1 | Q 1 | Page 10

1+ 3+ 53 + 73 + ...

Ex. 21.1 | Q 2 | Page 10

22 + 42 + 62 + 82 + ...

Ex. 21.1 | Q 3 | Page 10

1.2.5 + 2.3.6 + 3.4.7 + ...

Ex. 21.1 | Q 4 | Page 10

1.2.4 + 2.3.7 +3.4.10 + ...

Ex. 21.1 | Q 5 | Page 10

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

Ex. 21.1 | Q 6 | Page 10

1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...

Ex. 21.1 | Q 7 | Page 10

3 × 12 + 5 ×22 + 7 × 32 + ...

Ex. 21.1 | Q 8.1 | Page 10

Find the sum of the series whose nth term is:

2n2 − 3n + 5

Ex. 21.1 | Q 8.2 | Page 10

Find the sum of the series whose nth term is:

2n3 + 3n2 − 1

Ex. 21.1 | Q 8.3 | Page 10

Find the sum of the series whose nth term is:

n3 − 3n

Ex. 21.1 | Q 8.4 | Page 10

Find the sum of the series whose nth term is:

n (n + 1) (n + 4)

Ex. 21.1 | Q 8.5 | Page 10

Find the sum of the series whose nth term is:

(2n − 1)2

Ex. 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 + ...

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

Ex. 21.2 | Q 1 | Page 18

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

Ex. 21.2 | Q 2 | Page 18

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

Ex. 21.2 | Q 3 | Page 18

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

Ex. 21.2 | Q 4 | Page 18

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

Ex. 21.2 | Q 5 | Page 18

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

Ex. 21.2 | Q 6 | Page 18

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

Ex. 21.2 | Q 7 | Page 18

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

Ex. 21.2 | Q 8 | Page 18

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

Ex. 21.2 | Q 9 | Page 18

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

Ex. 21.2 | Q 10 | Page 18

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

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

Q 1 | Page 18

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

Q 2 | Page 18

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

Q 3 | Page 19

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

Q 4 | Page 19

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

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.

Q 6 | Page 19

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

Q 7 | Page 19

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

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 $\sum^n_{r = 1} \frac{S_r}{s_r}$ .

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

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

• $\sqrt{2n + 1}$

• $\frac{1}{2}\sqrt{2n + 1}$

• $\sqrt{2n + 1} - 1$

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

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

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

Q 4 | Page 19

If ∑ n = 210, then ∑ n2 =

•  2870

• 2160

• 2970

• none of these

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

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

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

Q 8 | Page 20

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

• $121 (\sqrt{6} + \sqrt{2})$

• $243 (\sqrt{3} + 1)$

• $\frac{121}{\sqrt{3} - 1}$

• $242 (\sqrt{3} - 1)$

Q 9 | Page 20

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

• $\frac{n (n + 1) (2n + 1)}{2}$

• $\frac{n (2n - 1) (2n + 1)}{3}$

• $\frac{(n - 1 )^2 (2n + 1)}{6}$

• $\frac{(2n + 1 )^3}{3}$

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

Ex. 21.1Ex. 21.2Others

## 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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