Question

The value of \[ 1! + 2! + 2! + 3! + 3! + \cdots + n \cdot n! \] is:

• A. \( (n!) \)
• B. \( (n + 1)! \)
• C. \( (n! + 1)! - 1 \)
• D. None of these

Hint:

When summing factorials, always consider possible simplifications and identities to evaluate the sum.

Answer 1

The Correct Option is C

We are asked to find the value of the sum: \[ 1! + 2! + 2! + 3! + 3! + \cdots + n \cdot n! \] We can use the following identity for the sum: \[ S = n! + 1! \] Thus, the correct answer is \( (n! + 1)! - 1 \).