# CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

###### CAT Questions | Algebra | Functions - Value of a Sequence
CAT Questions

The question is about Value of a Sequence. A question that combines greatest integer function and sequence. We need to find out the sum of the sequence. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 15: If [X] – Greatest integer less than or equal to x. Find the value of
[√1] + [√2] + [√3] +……………………………………………………+ [√100]

1. 615
2. 625
3. 5050
4. 505

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##### Method of solving this CAT Question from CAT Algebra - Functions: Combo of Sequence and Functions

As can be seen,
Thus, the series becomes:

3 * 1 + 5 * 2 + ……………………………………+ 19 * 9 + 10
=> ∑(2n+1)n + 10 (where, n = 1 to 9)
=> ∑ 2n2 + ∑n + 10
=> 2 * n (n+1) * $$frac{$2n + 1$}{6}$ + n * $\frac{$n + 1$}{2}$ + 10 => 2 * 9 * 10 * $\frac{19}{6}\\$ + 9 * $\frac{10}{2}\\$ + 10 => 570 + 45 + 10 => 625 The question is "Find the value of [√1] + [√2] + [√3] +……………………………………………………+ [√100]?" ##### Hence the answer is "625" Choice B is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Functions Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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