CAT Practice : Functions

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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

 

  • Correct Answer
    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) * + n * + 10
=) 2 x 9 x 10 x
=) 570 + 45 + 10 =) 625
Answer choice (B).


Correct Answer: 625



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