For any real number x, let [x] be the largest integer less than or equal to x. If ∑(n=1 to N)[√(5 + n/25)] = 25, then N is

Question

UPSC Quizroom · Accepted Answer

Given:
∑(n=1 to N) [1/5 + n/25] = 25

Simplify:
[1/5 + n/25] = [(n + 5)/25]

Now find the value of [(n + 5)/25] for different ranges of n:

Range of n	Count of n	Value of [(n + 5)/25]
1 to 19	19	0
20 to 44	25	1
45 to 69	25	2
...	...	...

Now calculate the sum:

Sum = 19(0) + 25(1) = 25

So, when N = 44, the sum equals 25.

Final Answer: N = 44

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