Question

For real number x, int(x) denotes integer part of x.int(x) is the largest integer less than or equal to x.int(1,2)=1,int(-2,4)=-3. find the value of int(1/2)+int(1/2+ 100)+int(1/2+2/100)+....+int(1/2+99/100)

Answer 1

Thank you for asking this question.

Here is your answer:

from int(1/2)+int(1/2+1/100)+....int(1/2+49/100) each term is less than 1 so  

int(1/2)+int(1/2+1/100)++....int(1/2+49/100) = 0

From int(1/2+50/100)+int(1/2+51/100)+...+int(1/2+99/100) ,each term has a value greater than 1 except int(1/2+50/100)= int(1)=1

From 50 to 99 each gives a value 1

int(1/2)+int(1/2+1/100)+int(1/2+2/100)... .int(1 /2+99/100)= 1+1+..+ 50 times

= 50

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