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

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

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Grade:12

1 Answers

Asish Mahapatra
36 Points
9 years ago
[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 rth 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 

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