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

Question

The inequality n + 1C 6 + nC 4 > n + 2C 5 - nC 5 holds true for all n greater than (A) 8 (B) 9 (C) 7 (D) 1

Tardigrade Admin · Accepted Answer

n + 1C6+ nC4+ nC5> n + 2C5 ⇒ n + 1C6+ n + 1C5> n + 2C5 ⇒ n + 2C6> n + 2C5 ⇒ ((n + 2) !/6 ! (n - 4) !)>((n + 2) !/5 ! (n - 3) !) ⇒ (1/6)>(1/(n - 3)) ⇒ n-3>6 ⇒ n>9

Q. The inequality $_^{n + 1} C_{6} +_^{n} C_{4} >_^{n + 2} C_{5} -_^{n} C_{5}$ holds true for all $n$ greater than

$8$

$9$

$7$

$1$

Q. The inequality _n+1C6​+_nC4​>_n+2C5​−_nC5​ holds true for all n greater than

8

9

7

1

_n+1C6​+_nC4​+_nC5​>_n+2C5​ ⇒_n+1C6​+_n+1C5​>_n+2C5​ ⇒_n+2C6​>_n+2C5​ ⇒6!(n−4)!(n+2)!​>5!(n−3)!(n+2)!​ ⇒61​>(n−3)1​ ⇒n−3>6 ⇒n>9

Q. The inequality $_^{n + 1} C_{6} +_^{n} C_{4} >_^{n + 2} C_{5} -_^{n} C_{5}$ holds true for all $n$ greater than

$8$

$9$

$7$

$1$