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FIND THE VALUE OF [1/2]+[1/2+1/1000]+...........[1/2+2946/1000] [.] denotes for GIF......GREATEST INTEGER FACTOR ?

FIND THE VALUE OF [1/2]+[1/2+1/1000]+...........[1/2+2946/1000]


[.] denotes for GIF......GREATEST INTEGER FACTOR ?

Grade:12

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

Dear Manoj

We have to divide the series in parts

  1. [1/2]+[1/2 + 1/1000] +.................+ [1/2 + 499/1000]=0
  2. [1/2 + 500/1000]+...........+ [1/2 + 1499/1000] = 1000 * 1=1000
  3. [1/2 + 1500/1000]+...........+ [1/2 + 2499/1000] = 1000 * 2=2000
  4. [1/2 + 2500/1000]+...........+ [1/2 + 2946/1000] = 447 * 3=1341

adding all

0 + 1000 + 2000 + 1341 = 4341 Answer

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AKASH GOYAL
AskiitiansExpert-IITD

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