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1 + 1 x 1! + 2 × 2! + 3 × 3! +. . . .+ n × n! =

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(n - 1)!

(n + 1)!

n × (n + 1)!

answer is C.

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Detailed Solution

1 + 1 × 11! + 2 × 2! + 3 × 3! + . . . . . + n × n!

= 1 +(2 - 1)1! + (3 - 1)2! +(4 - l)3! . .... + (n + 1 - 1)n!

= 1 +2 × 1! - 1! + 3 × 2! - 2! + 4 × 3! - 3! +. . . . + (n + 1)n! - n!

= 1 +2! - 1!+3! - 2! +4! - 3!+. . . .+ (n + 1)! - n!.= (n + 1)!.

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