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I want to calculate the sum of this series:

$$S = 1\cdot1! + 2\cdot2! + 3\cdot3! + 4\cdot4! +\dots+ n\cdot n!$$

Is their any formula for finding this sum?

user3786422
  • 245

1 Answers1

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Hint

$$kk!=(k+1)k!-k!=(k+1)!-k!$$ and telescope.