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Chapters
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](/images/mathematics-english-class-11_6:972cafaba17f4949992ada196fa0f041.jpg "RD Sharma solutions for Mathematics [English] Class 11 chapter 21 - Some special series")
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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.
RD Sharma solutions for Mathematics [English] Class 11 21 Some special series Exercise 21.1 [Page 10]
13 + 33 + 53 + 73 + ...
22 + 42 + 62 + 82 + ...
1.2.5 + 2.3.6 + 3.4.7 + ...
1.2.4 + 2.3.7 +3.4.10 + ...
1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ...
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...
3 × 12 + 5 ×22 + 7 × 32 + ...
Find the sum of the series whose nth term is:
2n2 − 3n + 5
Find the sum of the series whose nth term is:
2n3 + 3n2 − 1
Find the sum of the series whose nth term is:
n3 − 3n
Find the sum of the series whose nth term is:
n (n + 1) (n + 4)
Find the sum of the series whose nth term is:
(2n − 1)2
Find the 20th term and the sum of 20 terms of the series 2 × 4 + 4 × 6 + 6 × 8 + ...
RD Sharma solutions for Mathematics [English] Class 11 21 Some special series Exercise 21.2 [Page 18]
3 + 5 + 9 + 15 + 23 + ...
2 + 5 + 10 + 17 + 26 + ...
1 + 3 + 7 + 13 + 21 + ...
3 + 7 + 14 + 24 + 37 + ...
1 + 3 + 6 + 10 + 15 + ...
1 + 4 + 13 + 40 + 121 + ...
4 + 6 + 9 + 13 + 18 + ...
2 + 4 + 7 + 11 + 16 + ...
\[\frac{1}{1 . 4} + \frac{1}{4 . 7} + \frac{1}{7 . 10} + . . .\]
\[\frac{1}{1 . 6} + \frac{1}{6 . 11} + \frac{1}{11 . 14} + \frac{1}{14 . 19} + . . . + \frac{1}{(5n - 4) (5n + 1)}\]
RD Sharma solutions for Mathematics [English] Class 11 21 Some special series Exercise 21.3 [Pages 18 - 19]
Write the sum of the series 2 + 4 + 6 + 8 + ... + 2n.
Write the sum of the series 12 − 22 + 32 − 42 + 52 − 62 + ... + (2n − 1)2 − (2n)2.
Write the sum to n terms of a series whose rth term is r + 2r.
If \[\sum^n_{r = 1} r = 55, \text{ find } \sum^n_{r = 1} r^3\] .
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.
Write the sum of 20 terms of the series \[1 + \frac{1}{2}(1 + 2) + \frac{1}{3}(1 + 2 + 3) + . . . .\]
Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...
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 Mathematics [English] Class 11 21 Some special series Exercise 21.4 [Pages 19 - 20]
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
\[\sqrt{2n + 1}\]
\[\frac{1}{2}\sqrt{2n + 1}\]
\[\sqrt{2n + 1} - 1\]
\[\frac{1}{2}\left\{ \sqrt{2n + 1} - 1 \right\}\]
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
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
If ∑ n = 210, then ∑ n2 =
2870
2160
2970
none of these
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
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
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
The sum of 10 terms of the series \[\sqrt{2} + \sqrt{6} + \sqrt{18} +\] .... is
\[121 (\sqrt{6} + \sqrt{2})\]
\[243 (\sqrt{3} + 1)\]
\[\frac{121}{\sqrt{3} - 1}\]
\[242 (\sqrt{3} - 1)\]
The sum of the series 12 + 32 + 52 + ... to n terms is
\[\frac{n (n + 1) (2n + 1)}{2}\]
\[\frac{n (2n - 1) (2n + 1)}{3}\]
\[\frac{(n - 1 )^2 (2n + 1)}{6}\]
\[\frac{(2n + 1 )^3}{3}\]
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
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.
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Concepts covered in Mathematics [English] Class 11 chapter 21 Some special series are Sequence, Series, and Progression, Sum to' n' Terms of a Geometric Progression, Geometric Progression (G. P.), Relationship Between A.M. and G.M., Arithmetic Progression (A.P.).
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.
