Observe that
[+] = 0
if 0 <
+ < 1
or K <
= 66.66
∴ K = 0 , 1 , 2 , 3 , .... , 66
if 67 ≤ K ≤ 99 observe that
1 <
+ ≤
+ ≤
+ < 2
→
[+] = 1
∴
[+] = 0 for K = 1 , 2 , 3 , ...... 66 and
= 1 for K = 67 , 68 , ..... , 99
∴ S = (0 + 0 + ..... 67 terms) + (1 + 1 + ..... 33 terms) = 33