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_ k=1 ²⁰ k k !is equal to

Options

  1. A21 !
  2. B20 ! + 1
  3. C21!-1
  4. D20!-1

Correct answer

C. 21!-1

Step-by-step solution

We have, _ k=1 ²⁰ k k ! aligned _ k=1 ²⁰ k k! & = _ k=1 ²⁰(k+1-1) k!= _ k=1 ²⁰[(k+1) k!-k!] & = _ k=1 ²⁰(k+1)!- _ k=1 ²⁰ k![ (n+1) n!=(n+1)! & =2!-1!+3!-2!+21!-3!+ +21!-20! & =21!-1 aligned

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