The numbers of elements in the set { n ∈ { 1 , 2 , 3 , . . . . 1 0 0 } | ( 1 1 ) n > ( 1 0 ) n + ( 9 ) n } is………….

1 1 n − 9 n > 1 0 n ⇒ ( 1 0 + 1 ) n − ( 1 0 − 1 ) n > 1 0 n ->For n ≥ 5 the inequality Satisfies. For n= 4. 2 [4 * 103 + 4 * 10] > 104 ->8 * 1010 > 104 which is a contradiction ∴ n ≥ 5 all values satisfies. Hence possible values of n is 96

The numbers of elements in the set ${n \in {1, 2, 3, . . . . 100} | {(11)}^{n} > {(10)}^{n} + {(9)}^{n}}$ is………….

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Alok Kumar Singh | Contributor-Level 10

7 months ago

$1 1^{n} - 9^{n} > 1 0^{n}$

$\Rightarrow {(10 + 1)}^{n} - {(10 - 1)}^{n} > 1 0^{n}$

->For $n \geq 5$ the inequality Satisfies.

For n= 4. 2 [4 * 10³ + 4 * 10] > 10⁴

->8 * 1010 > 10⁴ which is a contradiction

$∴ n \geq 5$ all values satisfies. Hence possible values of n is 96

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