Write the expression n C r -1- n C r -1-2 - n C r in the simplest form-

^nC_r+1 + ^nC_r 1 + 2 × ^nC_r = (^nC_r+1 + ^nC_r) + ^nC_r + ^nC_r 1 = ^n+1C_r+1 + ^n+1C_r {Since ^nC_r + ^nC_r 1 = ^n+1C_r} = ^(n+1)+1C_(r+1) = ...

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nCr Definitions and Properties

Write the exp...

Question

Write the expression $^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}$ in the simplest form.

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^{n + 4} C_{r} -^{n} C_{r} - {3.}^{n} C_{r - 1} - 3^{n} C_{r - 2} -^{n} C_{r - 3}

^{n} C_{r}

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^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}

^{n} C_{r} + {4.}^{n} C_{r - 1} + {6.}^{n} C_{r - 2} + {4.}^{n} C_{r - 3} +^{n} C_{r - 4} =

^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}

\frac{^{n} C_{r}}{^{n} C_{r + 1}} = \frac{1}{2}

\frac{^{n} C_{r + 1}}{^{n} C_{r + 2}} = \frac{2}{3}

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