# Ex 9.4, 10

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 9.4, 10 Find the sum to n terms of the series whose nth terms is given by (2n 1)2 Given an = (2n 1)2 =(2n)2 + (1)2 2(2n)(1) = 4n2 + 1 4n = 4n2 4n + 1 Sum of n terms is = 4((n(n+1)(2n+1))/6) 4 (n(n+1)/2) + n = n ("4" (n(n+1)(2n+1))/6 " 4" ( ( + 1))/2 " + 1" ) = n (2/3 " (n + 1)(2n + 1) 2(n + 1) + 1" ) = n ((2(n + 1)(2n + 1) 6(n + 1) + 3)/3) = /3 [(2n + 2)(2n + 1) 6n 6 + 3 ] = /3 [4n2 + 2n + 4n + 2 6n 3] = /3 [4n2 + 6n 6n 1] = /3 [4n2 1] = /3 [(2n)2 (1)2] = /3 [(2n 1) (2n + 1)] Hence, the required sum is /3 [(2n 1 ) (2n + 1)]

Example 6
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Ex 9.2, 5 Important

Ex 9.2, 9 Important

Ex 9.2, 15 Important

Ex 9.2, 17 Important

Example 14 Important

Example 15 Important

Ex 9.3, 3 Important

Ex 9.3, 11 Important

Ex 9.3, 17 Important

Ex 9.3, 18 Important

Ex 9.3, 22 Important

Ex 9.3, 28 Important

Ex 9.3, 29 Important

Ex 9.4.4 Important

Ex 9.4, 7 Important

Ex 9.4, 9 Important

Ex 9.4, 10 Important You are here

Example 23 Important

Misc 16 Important

Misc 19 Important

Misc 25 Important

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Misc 32 Important

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.