please explain fully …...please …...hey image attached please tell the method which is used in solution …..please sir .maam …..please anyone …...

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

 

Clearly [x] is 0 if x lies between 0 and 1 (exclusive) and [x] = 1 if x lies between 1 (inclusive) and 2 (exclusive)

 

In this case, the r^th term is 

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+ (r-1)/100 = 1

 

Thus from r = 26, to r = 100, each term evaluates to 1.

So, the sum will be equal to: how many numbers are between 26 and 100 (both inclusive) = 100 – 26 + 1 = 75