What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . . n × n!
where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1
a) n × (n – 1) × (n – 1)!
b) (n + 1)! – {n × (n – 1)}
c) (n + 1)! – n!
d) (n + 1)! – 1!
Answer: d
Explanation: 1 × 1! = (2 – 1) × 81! = 2 × 1! – 1 × 1! = 2! – 1!
2 × 2! = (3 – 1) × 2! = 3 × 2! – 2! = 3! – 2!
3 × 3! = (4 – 1) × 3! = 4 × 3! – 3! = 4! – 3!
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n × n! = (n + 1 – 1) × n! = (n + 1) (n!) – n! = (n + 1)! – n!
Summing up all these terms, we get (n + 1)! – 1!
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