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KVPY2011MathematicsSets and Relations

The sum of (1²-1+1 )(1 !)+ (2²-2+1 )(2 !)+ .+ (n²-n+1 )(n !) is -

Options

  1. A(n+2) !
  2. B(n-1)((n+1) !)+1
  3. C(n+2) !-1
  4. Dn((n+1) !)-1

Correct answer

B. (n-1)((n+1) !)+1

Step-by-step solution

T _ n = ( n ²- n +1 ) n ! = ( n ²-1 ) n !-( n -2) n ! T _ n =( n -1)( n +1) !-( n -2) n ! Sum =1+( n -1)( n +1) !

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