What is the value of 1 - 1 -2 - 2 -3 - 3 - n - n - where n- means n factorial or nn-1n-2 - 1A- n-1 -B- n-1C- n -D- None of theseE- n-1 -1

The correct option is E (n+1)! 1 n*n! = (n+1 1)*n! = (n+1)! n! So ∑n*n! = (n+1)! 1 ...

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What is the value of $1 \times 1! + 2 \times 2! + 3 \times 3! + . . . . . . . . . . . . n \times n!$ ; where n! means n factorial or n(n-1)(n-2)...1

(n+1)!-1

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(n+1)!

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n!-1

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None of these

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What is the value of $1 \times 1! + 2 \times 2! + 3 \times 3! + . . . . . . . . . . . . n \times n!$ ; where n! means n factorial or n(n-1)(n-2)...1

2 \leq {(1 + \frac{1}{n})}^{n} < 3, n \geq 1

n^{n + 1} > (n + 1)^{n}, n \geq 3, n ϵ N

n

n^{n + 1} - n {(n - 1)}^{n + 1} + \frac{n (n - 1)}{2!} {(n - 2)}^{n + 1} - \dots = \frac{1}{2} n (n + 1)!

n^{n} - (n + 1) {(n - 1)}^{n} + \frac{(n + 1) n}{2!} {(n - 2)}^{n} - \dots = 1

n

1^{n} - n 2^{n} + \frac{n (n - 1)}{1 \cdot 2} 3^{n} - \dots = {(- 1)}^{n} n!

{(n + p)}^{n} - n {(n + p - 1)}^{n} + \frac{n (n - 1)}{2!} {(n + p - 2)}^{n} - \dots = n!

n + 1

{¯ x}_{2}

{¯ x}_{2} - {¯ x}_{1}

The value of $C_{0} + 3 C_{1} + 5 C_{2} + 7 C_{3} + . . . . + (2 n + 1) C_{n}$ is equal to :

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