CAT 2024 Slot 1 QA Question 22

Type-in-the-answer (no negative marking) · Number Systems · Miscellaneous · Try it, then check the answer and solution below.

For any natural number

n , let

a_{n}

be the largest integer not exceeding \sqrt{n}

. Then the value of

a_{1}+a_{2}+\ldots .+a_{50}

TITA Answer:

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Official Convenor Answer Key: 217

Answer and solution

Answer: 217

To find the value of

a_{1} + a_{2} + \ldots + a_{50} , where

a_{n}

is the largest integer not exceeding \sqrt{n} , we need to consider the behavior of the floor function. For each integer

k , the value

a_{n} = k

for

n

in the range

k^2 \leq n < (k+1)^2

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