The inequality C n + 1 6 + C n 4 C n + 2 5 − C n 5 holds true for all n greater than

Question

The inequality C n + 1 6 + C n 4 > C n + 2 5 − C n 5 holds true for all n greater than, 8, 9, 7, 1

MARKS App · Accepted Answer

C n + 1 6 + C n 4 + C n 5 > C n + 2 5 ⇒ C n + 1 6 + C n + 1 5 > C n + 2 5 ⇒ C n + 2 6 > C n + 2 5 ⇒ n + 2 ! 6 ! n - 4 ! > n + 2 ! 5 ! n - 3 ! ⇒ 1 6 > 1 n - 3 ⇒ n - 3 > 6 ⇒ n > 9

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