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The sum $1 \times 1!+2 \times 2!+\ldots+50 \times 50$ ! equals
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Verified Answer
The correct answer is:
$51 !-1$
$1 \times 1!+2 \times 2!+\ldots+50 \times 50!$
$=(2-1) 1!+(3-1) 2!+(4-1) 3 !$
$+\ldots+(51-1) 50!$
$=(2 !-1!)+(3 !-2!)+(4 !-3 !)+(51!-50!)$
$+\ldots+(511-501)$
$=511-11=511-1$
$=(2-1) 1!+(3-1) 2!+(4-1) 3 !$
$+\ldots+(51-1) 50!$
$=(2 !-1!)+(3 !-2!)+(4 !-3 !)+(51!-50!)$
$+\ldots+(511-501)$
$=511-11=511-1$
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