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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: Trigonometric equations
11: Mathematical Induction
12: Complex Numbers
13: Quadratic Equations
14: Linear Inequations
15: Permutations
16: Combinations
17: Binomial Theorem
Chapter 18: Sequences and Series
▶ 19: Some special series
20: Brief review of cartesian system of rectangular co-ordinates
21: The straight lines
22: The circle
23: Parabola
24: Ellipse
25: Hyperbola
26: Introduction to three dimensional coordinate geometry
27: Limits
28: Derivatives
29: Statistics
30: Probability
![R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ chapter 19 - Some special series - Shaalaa.com](/images/mathematics-english-class-11_6:95ccb2cc0fae4d15b2094353f6131b62.jpg "R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ chapter 19 - Some special series")
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Solutions for Chapter 19: Some special series
Below listed, you can find solutions for Chapter 19 of CBSE, Karnataka Board PUC R.D. Sharma for माठेमटिक्स १ [इंग्रजी] इयत्ता ११.
R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ 19 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 + ...
R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ 19 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 + ...
\[\frac{1}{1 . 4} + \frac{1}{4 . 7} + \frac{1}{7 . 10} + . . .\]
\[\frac{1}{1 . 6} + \frac{1}{6 . 11} + \frac{1}{11 . 14} + \frac{1}{14 . 19} + . . . + \frac{1}{(5n - 4) (5n + 1)}\]
R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ 19 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 \[\sum^n_{r = 1} \frac{S_r}{s_r}\] .
R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ 19 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 19: Some special series
R.D. Sharma solutions for माठेमटिक्स १ [इंग्रजी] इयत्ता ११ chapter 19 - Some special series
Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics माठेमटिक्स १ [इंग्रजी] इयत्ता ११ 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. R.D. Sharma solutions for Mathematics माठेमटिक्स १ [इंग्रजी] इयत्ता ११ CBSE, Karnataka Board PUC 19 (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. R.D. Sharma textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in माठेमटिक्स १ [इंग्रजी] इयत्ता ११ chapter 19 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 R.D. Sharma माठेमटिक्स १ [इंग्रजी] इयत्ता ११ 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 R.D. Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC माठेमटिक्स १ [इंग्रजी] इयत्ता ११ students prefer R.D. Sharma Textbook Solutions to score more in exams.
Get the free view of Chapter 19, Some special series माठेमटिक्स १ [इंग्रजी] इयत्ता ११ additional questions for Mathematics माठेमटिक्स १ [इंग्रजी] इयत्ता ११ CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.
