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Question 66
For any real number x, let [x] be the largest integer less than or equal to x. If $$\sum_{n=1}^N \left[\frac{1}{5} + \frac{n}{25}\right] = 25$$ then N is
Correct Answer: 44
Solution
It is given,
$$\Sigma_{n=1}^N\ \left[\frac{1}{5}+\frac{n}{25}\right]=25$$
$$\Sigma_{n=1}^N\ \left[\frac{5+n}{25}\right]=25$$
For n = 1 to n = 19, value of function is zero.
For n = 20 to n = 44, value of function will be 1.
44 = 20 + n - 1
n = 25 which is equal to given value.
This implies N = 44
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Your Doubts
sir is my method wrong? I have tried using this method but couldn't arrive at answer because in most questions where summation is asked we could solve them through this approach right? please help
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