જો left( {_3^n} right) + left( {_4^n} ri | vedclass

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Question

$\left( {\begin{array}{*{20}{c}}
  n \ 
  3 
\end{array}} ight) + \left( {\begin{array}{*{20}{c}}
  n \

Vedclass · Accepted Answer

$n > 6$

Vedclass · Answer

$\left( {\begin{array}{*{20}{c}} n \ 3 \end{array}} ight) + \left( {\begin{array}{*{20}{c}} n \ 4 \end{array}} ight) > \left( {\begin{array}{*{20}{c}} {n + 1} \ 3 \end{array}} ight)$ $\left( {\begin{array}{*{20}{c}} {n + 1} \ 4 \end{array}} ight) > \left( {\begin{array}{*{20}{c}} {n + 1} \ 3 \end{array}} ight)$ $\frac{{(n + 1)\,!}}{{4\,!\,(n - 3)\,!}} > \,\frac{{(n + 1)\,!}}{{3\,!\,(n - 2)\,!}}\,\,$ $\,\,\frac{{(n + 1)\,!}}{{4\,(3\,!)(n - 3)\,!}} > \,\frac{{(n + 1)\,!}}{{3\,!\,(n - 2)(n - 3)\,!}}\,\,\,$ $\,\,\frac{1}{4} > \frac{1}{{n - 2}}\,\,$ $4 < n - 2$ $6 < n$ $\,\,n > 6$

જો $\left( {_3^n} \right) + \left( {_4^n} \right) > \left( {_{\,\,\,3}^{n + 1}} \right)$ હોય, તો....

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