Commerce Exam > Commerce Notes > Mathematics (Maths) Class 11 > RD Sharma Class 11 Solutions Chapter - Some Special Series
RD Sharma Class 11 Solutions Chapter - Some Special Series
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 21. Some Special Series Exercise 21.1 1. Question Find the sum of the following series to n terms: 1 3 + 3 3 + 5 3 + 7 3 + …….. Answer nth term would be = 2n - 1 We know, Therefore, ………….equation 1 …………….equation 2 From equation 1 = [replace 2n by n] = Substituting in equation 2 2. Question Find the sum of the following series to n terms: 2 3 + 4 3 + 6 3 + 8 3 + ……… Answer Page 2 21. Some Special Series Exercise 21.1 1. Question Find the sum of the following series to n terms: 1 3 + 3 3 + 5 3 + 7 3 + …….. Answer nth term would be = 2n - 1 We know, Therefore, ………….equation 1 …………….equation 2 From equation 1 = [replace 2n by n] = Substituting in equation 2 2. Question Find the sum of the following series to n terms: 2 3 + 4 3 + 6 3 + 8 3 + ……… Answer nth term would be 2n We know ……(1) Therefore, Substituting the value from 1 3. Question Find the sum of the following series to n terms: 1.2.5 + 2.3.6 + 3.4.7 + …….. Answer The nth term be n(n + 1)(n + 4) Thus we can write 1.2.5 + 2.3.6 + 3.4.7 + …….. The general term would be r(r + 1)(r + 4) We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 Thus, = ……(1) We know Substituting in (1) Page 3 21. Some Special Series Exercise 21.1 1. Question Find the sum of the following series to n terms: 1 3 + 3 3 + 5 3 + 7 3 + …….. Answer nth term would be = 2n - 1 We know, Therefore, ………….equation 1 …………….equation 2 From equation 1 = [replace 2n by n] = Substituting in equation 2 2. Question Find the sum of the following series to n terms: 2 3 + 4 3 + 6 3 + 8 3 + ……… Answer nth term would be 2n We know ……(1) Therefore, Substituting the value from 1 3. Question Find the sum of the following series to n terms: 1.2.5 + 2.3.6 + 3.4.7 + …….. Answer The nth term be n(n + 1)(n + 4) Thus we can write 1.2.5 + 2.3.6 + 3.4.7 + …….. The general term would be r(r + 1)(r + 4) We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 Thus, = ……(1) We know Substituting in (1) 4. Question Find the sum of the following series to n terms: 1.2.4 + 2.3.7 + 3.4.10 + ………… Answer The nth term be n(n + 1)(3n + 1) 1.2.4 + 2.3.7 + 3.4.10 + …………= We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 …..(1) We know Thus from (1) 5. Question Find the sum of the following series to n terms: 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ……… Answer The nth term be Where = (n - 0) + (n - 1) + (n - 2) + …… + (n - n) Page 4 21. Some Special Series Exercise 21.1 1. Question Find the sum of the following series to n terms: 1 3 + 3 3 + 5 3 + 7 3 + …….. Answer nth term would be = 2n - 1 We know, Therefore, ………….equation 1 …………….equation 2 From equation 1 = [replace 2n by n] = Substituting in equation 2 2. Question Find the sum of the following series to n terms: 2 3 + 4 3 + 6 3 + 8 3 + ……… Answer nth term would be 2n We know ……(1) Therefore, Substituting the value from 1 3. Question Find the sum of the following series to n terms: 1.2.5 + 2.3.6 + 3.4.7 + …….. Answer The nth term be n(n + 1)(n + 4) Thus we can write 1.2.5 + 2.3.6 + 3.4.7 + …….. The general term would be r(r + 1)(r + 4) We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 Thus, = ……(1) We know Substituting in (1) 4. Question Find the sum of the following series to n terms: 1.2.4 + 2.3.7 + 3.4.10 + ………… Answer The nth term be n(n + 1)(3n + 1) 1.2.4 + 2.3.7 + 3.4.10 + …………= We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 …..(1) We know Thus from (1) 5. Question Find the sum of the following series to n terms: 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ……… Answer The nth term be Where = (n - 0) + (n - 1) + (n - 2) + …… + (n - n) Since, ………(1) 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ………….= From (1) 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ……….. Thus, solving Solving We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 Thus, We know, Substituting Page 5 21. Some Special Series Exercise 21.1 1. Question Find the sum of the following series to n terms: 1 3 + 3 3 + 5 3 + 7 3 + …….. Answer nth term would be = 2n - 1 We know, Therefore, ………….equation 1 …………….equation 2 From equation 1 = [replace 2n by n] = Substituting in equation 2 2. Question Find the sum of the following series to n terms: 2 3 + 4 3 + 6 3 + 8 3 + ……… Answer nth term would be 2n We know ……(1) Therefore, Substituting the value from 1 3. Question Find the sum of the following series to n terms: 1.2.5 + 2.3.6 + 3.4.7 + …….. Answer The nth term be n(n + 1)(n + 4) Thus we can write 1.2.5 + 2.3.6 + 3.4.7 + …….. The general term would be r(r + 1)(r + 4) We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 Thus, = ……(1) We know Substituting in (1) 4. Question Find the sum of the following series to n terms: 1.2.4 + 2.3.7 + 3.4.10 + ………… Answer The nth term be n(n + 1)(3n + 1) 1.2.4 + 2.3.7 + 3.4.10 + …………= We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 …..(1) We know Thus from (1) 5. Question Find the sum of the following series to n terms: 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ……… Answer The nth term be Where = (n - 0) + (n - 1) + (n - 2) + …… + (n - n) Since, ………(1) 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ………….= From (1) 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ……….. Thus, solving Solving We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 Thus, We know, Substituting Thus the answer is 6. Question Find the sum of the following series to n terms: 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …………. Answer The last term be n(n + 1) The generalized equation be ……………….(1) Since We know by property that: ?ax n + bx n - 1 + cx n - 2 …….d 0 =a?x n + b?x n - 1 + c?x n - 2 …….. + d 0 ?1 We know Thus substituting in (1) 7. Question Find the sum of the following series to n terms: 3 × 1 2 + 5 × 2 2 + 7 × 3 2 + ………….. Answer The nth term will be n 2 ×(2n + 1) The generalized equation beRead More
About this Document
4.87/5 Rating
Apr 29, 2026 Last updated
Document Description: RD Sharma Class 11 Solutions Chapter - Some Special Series for Commerce 2026 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Class 11 Solutions Chapter - Some Special Series have been prepared according to the Commerce exam syllabus. Information about RD Sharma Class 11 Solutions Chapter - Some Special Series covers topics like and RD Sharma Class 11 Solutions Chapter - Some Special Series Example, for Commerce 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 11 Solutions Chapter - Some Special Series.
Introduction of RD Sharma Class 11 Solutions Chapter - Some Special Series in English is available as part of our Mathematics (Maths) Class 11 for Commerce & RD Sharma Class 11 Solutions Chapter - Some Special Series in Hindi for Mathematics (Maths) Class 11 course. Download more important topics related with notes, lectures and mock test series for Commerce Exam by signing up for free. Commerce: RD Sharma Class 11 Solutions Chapter - Some Special Series
Description
RD Sharma Class 11 Solutions Chapter of Maths Class 11 on EduRev - covers important questions, MCQs with answers. Helps you prepare for exam.
Information about RD Sharma Class 11 Solutions Chapter - Some Special Series
In this doc you can find the meaning of RD Sharma Class 11 Solutions Chapter - Some Special Series defined & explained in the simplest way possible. Besides explaining types of RD Sharma Class 11 Solutions Chapter - Some Special Series theory, EduRev gives you an ample number of questions to practice RD Sharma Class 11 Solutions Chapter - Some Special Series tests, examples and also practice Commerce tests
Related Searches
Previous Year Questions with Solutions, Important questions, RD Sharma Class 11 Solutions Chapter - Some Special Series, study material, Viva Questions, MCQs, practice quizzes, ppt, Sample Paper, video lectures, past year papers, mock tests for examination, Free, Semester Notes, RD Sharma Class 11 Solutions Chapter - Some Special Series, Objective type Questions, shortcuts and tricks, Exam, Extra Questions, pdf , RD Sharma Class 11 Solutions Chapter - Some Special Series, Summary;