If ^n C_3 + ,^n C_4 > ,^ n + 1 C_3 , then - Vidyadip

MCQ

If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then

✓
$n > 6$
B
$n > 7$
C
$n < 6$
D
None of these

✓

Answer

Correct option: A.

$n > 6$

a
(a) ${}^n{C_3} + {}^n{C_4} > {}^{n + 1}{C_3}$

==>${}^{n + 1}{C_4} > {}^{n + 1}{C_3}\,\,(\,{}^n{C_r} + {}^n{C_{r + 1}} = {}^{n + 1}{C_{r + 1}})$

==> $\frac{{{}^{n + 1}{C_4}}}{{{}^{n + 1}{C_3}}} > 1$

==> $\frac{{n - 2}}{4} > 1$

$ \Rightarrow n > 6$.

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