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COMEDK2023MathematicsSequences and Series

The value of 1 2 ! + 2 3 ! + + 99 100 ! is equal to

Options

  1. A100 !-1 100 !
  2. B100 !+1 100 !
  3. C999 !-1 999 !
  4. D999 !+1 999 !

Correct answer

A. 100 !-1 100 !

Step-by-step solution

aligned & Given, 1 2 ! + 2 3 ! + + 99 100 ! & = 2-1 2 ! + 3-1 3 ! + 4-1 4 ! + + 100-1 100 ! & = ( 1 1 ! - 1 2 ! )+ ( 1 2 ! - 1 3 ! )+ ( 1 3 ! - 1 4 ! )+ + ( 1 99 ! - 1 100 ! ) & =1- 1 100 ! = 100 !-1 100 ! aligned

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