# CAT Practice : Functions

You are here: Home  CAT Questionbank   CAT Quant  Algebra: Functions  Question 17
Combo of Sequence and Functions

## Value of a Sequence

Q.17: 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

Choice B. 625

## Detailed Solution

As can be seen,
Thus, the series becomes:
3 x 1 + 5 x 2 + ……………………………………+ 19 x 9 + 10
=) ∑(2n+1)n + 10 (where, n = 1 to 9)
=) ∑ 2n2 + ∑n + 10
=) 2 x n (n+1) * $\frac{(2n + 1)}{6}$ + n * $\frac{(n + 1)}{2}$ + 10
=) 2 x 9 x 10 x $\frac{19}{6} + 9 x \frac{10}{2} + 10$
=) 570 + 45 + 10 =) 625

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Functions.