Find the value of n- if n - 1- - 12-n - 1-

(n+1)! = 12 × (n 1)! ⇒ (n+1) n (n 1) ! = 12 (n 1)! ⇒ n^2+n=12 ⇒ n^2+n 12=0 ⇒ n^2+4n 3n 12=0 #160; ⇒ n (n+4) 3 (n+4)=0 ⇒ ( ...

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Factorial

Find the valu...

Question

$Find the value of n, if (n + 1)! = 12 \times (n - 1)!$

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\frac{1}{1^{2}} + \frac{1}{2^{2}} + \dots + \frac{1}{{(n + 1)}^{2}} = \frac{1}{1 -} \frac{1^{4}}{1^{2} + 2^{2} -} \dots \frac{n^{4}}{n^{2} + {(n + 1)}^{2}}

1 + 2 + 3 + 4 + . . . . . + n = ?

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1 + 1 + 1 + 1 + . . . . . . + (n - 1) = ?

1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . + n^{2} = ?

1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . + {(n - 1)}^{2} = ?

{lim}_{n \to \infty} ⎡ ⎢ ⎢ ⎣ \frac{1}{n} + \frac{1}{\sqrt{n^{2} - 1^{2}}} + \frac{1}{\sqrt{n^{2} - 2^{2}}} + . . . . + \frac{1}{\sqrt{n^{2} - {(n - 1)}^{2}}} ⎤ ⎥ ⎥ ⎦

\frac{2}{3} + \frac{8}{9} + \frac{26}{27} + \frac{80}{81} +

n - \frac{1}{2} (3^{- n} - 1)

n - \frac{1}{2} (1 - 3^{- n})

n + \frac{1}{2} (3^{n} - 1)

n - \frac{1}{2} (3^{n} - 1)

n

(n + 1)! = 12 \times (n - 1)!

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