Q29 / 55 · KVPY 2020 (SA) · Mathematics

Let x be the greatest integer less than or equal to x, for a real number x. Then the following sum

22020+122018+1+32020+132018+1+42020+142018+1+52020+152018+1+62020+162018+1

is :-

  • A
    80
  • Correct answer
    B
    85
  • C
    90
  • D
    95

Solution

22020+122018+1=4.22018+122018+1=422018+1-322018+1

4-322018+1=t, 3<t<4

Now 22020+122018+1=3

similarly 32020+132018+1=9.32018+132018+1=9-832018+1

32020+132018+1=8

similarly n2020+122018+1=n2-1

22-1+32-1+42-1+52-1+62-1

=3+8+15+24+35=85

Hence, the correct answer is option: 'B'.

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