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

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Chapters

    1: Sets

    2: Relations

    3: Functions

    4: Measurement of Angles

    5: Trigonometric Functions

    6: Graphs of Trigonometric Functions

    7: Values of Trigonometric function at sum or difference of angles

    8: Transformation formulae

    9: Values of Trigonometric function at multiples and submultiples of an angle

    10: Sine and cosine formulae and their applications

    11: Trigonometric equations

    12: Mathematical Induction

    13: Complex Numbers

    14: Quadratic Equations

    15: Linear Inequations

    16: Permutations

    17: Combinations

    18: Binomial Theorem

    19: Arithmetic Progression

    20: Geometric Progression

▶ 21: Some special series

    22: Brief review of cartesian system of rectangular co-ordinates

    23: The straight lines

    24: The circle

    25: Parabola

    26: Ellipse

    27: Hyperbola

    28: Introduction to three dimensional coordinate geometry

    29: Limits

    30: Derivatives

    31: Mathematical reasoning

    32: Statistics

    33: Probability

RD Sharma solutions for Mathematics [English] Class 11 chapter 21 - Some special series - Shaalaa.com

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Solutions for Chapter 21: Some special series

Below listed, you can find solutions for Chapter 21 of CBSE, Karnataka Board PUC RD Sharma for Mathematics [English] Class 11.

Exercise 21.1Exercise 21.2Exercise 21.3Exercise 21.4

Exercise 21.1 [Page 10]

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

Exercise 21.1 | Q 1 | Page 10

1³+ 3³+ 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 20^th 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 Mathematics [English] Class 11 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 Mathematics [English] Class 11 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 r^th term is r + 2^r.

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 S_n denote the sum of the cubes of first n natural numbers and s_n 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 Mathematics [English] Class 11 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 S_n = \[\sum^n_{r = 1} \frac{1 + 2 + 2^2 + . . . \text { Sum to r terms }}{2^r}\], then S_n 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

\[n - \frac{1}{2}( 3^{- n} - 1)\]
\[n - \frac{1}{2}(1 - 3^{- n} )\]
\[n + \frac{1}{2}( 3^n - 1)\]
\[n - \frac{1}{2}( 3^n - 1)\]

Solutions for 21: Some special series

Exercise 21.1Exercise 21.2Exercise 21.3Exercise 21.4

RD Sharma solutions for Mathematics [English] Class 11 chapter 21 - Some special series - Shaalaa.com

RD Sharma solutions for Mathematics [English] Class 11 chapter 21 - Some special series

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC 21 (Some special series) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics [English] Class 11 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..

Using RD Sharma Mathematics [English] Class 11 solutions Some special series exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in RD Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Mathematics [English] Class 11 students prefer RD Sharma Textbook Solutions to score more in exams.

Get the free view of Chapter 21, Some special series Mathematics [English] Class 11 additional questions for Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.

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