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COMEDK2018MathematicsSequences and Series

The last digit of _ 1 < p < 100 p prime p !- _ n=1 ⁵⁰(2 n) ! is

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

A. 2

Step-by-step solution

1 < p < 100 p p r i m e P !- _ n=1 ⁵⁰(2 n !)=(2 !+3 !+5 !+7 !+ )-(2 !+4 !+6 !+ ) After 5 ! the number will have 0 at the one's place. So, they will no effect the last digit of the total sum. Now last digit of (2 !+3 !)=2+6=8 Last digit of (2 !+4 !)=2+4=6 Last digit of _ 1 < p < 100 p prime p !- _ n=1 ⁵⁰(2 m !)=8-6=2

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