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please explain fully …...

please explain fully …...

Question Image
Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

[x] is the greatest integer that is less than or equal to x.

[x] is 0 if x lies between 0 (included) and 1 (excluded)
[x] is 1 if x lies between 1 (included) and 2 (excluded)

In this case, the xthterm is
[\frac{3}{4}+\frac{x}{100}]
where x varies from 0 to 99 (both included)
This will be equal to zero till the value inside is atleast 1.
Note that the last term is [3/4 + 99/100] = [1.74] = 1.
So every term will equal 1, starting from the term where 3/4+ x/100 = 1
\frac{3}{4}+\frac{x}{100} = 1
x = 25
Thus from x = 25, to x = 99, each term evaluates to 1.
And from x = 0 to x = 24, each term equal to zero.
So, the sum will be equal to: how many numbers are between 25 and 99 (both included) = 99 – 25 + 1 = 75

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