If n -lim1-10n1-10n-1 - - -10 - then give the value of - is -

[ lim #160; #160;_ x→∞ #160; 1 ( 10 ) #160; ^ n / 1+10( 10 ^ n ) #160; = α #160; / 10 ...

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Algebra of Limits

If n →∞lim1...

Question

If $l i m n \to \infty \frac{1 - (10)^{n}}{1 + (10)^{n + 1}} = \frac{- α}{10},$ then give the value of $α$ is :

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Solution

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α

β

x^{2} - x - 1 = 0,

α

β

a_{n} = \frac{α^{n} - β^{n}}{α - β}, n \geq 1

b_{1} = 1

b_{n} = a_{n - 1} + a_{n + 1}, n \geq 2

n + 2 = 10 n - 1

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n \sum k = 1 (x + k - 1) (x + k) = 10 n,

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α + 1

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(\frac{1}{10})^{n} < 0.01

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(\frac{1}{10})^{n - 1} < 0.1

n^{4} < 10^{n}

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(n + 1)^{4} < 10^{n + 1}

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