CAT Quantitative Aptitude Questions | CAT Algebra - Functions 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

Explanatory Answer

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.