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Solution


Q.

The sum 1×1!+2×2!+...+50×50! equals
1 51!  
2 51!−1  
3 51!+1  
4 2×51!  

Ans.

(2)

1(1!)+2(2!)+⋯+50(50!)

=(2-1)(1!)+(3-1)(2!)+(4-1)(3!)+⋯+(51-1)(50!)

=(2!-1!)+(3!-2!)+(4!-3!)+⋯+(51!-50!)

=51!-1!=51!-1