Find the sum of 1.1! + 2.2! + 3.3! + ... + (n-1)(n-1)! + n. n!.

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(n - 1)!

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(n + 1)! - 1

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( n + 1)!

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Solution

The correct option is C
(n + 1)! - 1

Put n = 2
Given expression = 5
Option (a) = 2
Option (b) = 1
Option (c) = 5
Option (d) = 6
Hence option (c)

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lim n \to \infty \frac{1.1! + 2.2! + 3.3! + \dots + n . n!}{(n + 1)!} =

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1. (1!) + 2. (2!) + 3. (3!) + . . . . . . . . . . .

(n + k)! - m

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