Find the value of - n C r - n - 1 C r - - - r C r -

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Algebraic Identities

Find the valu...

Question

Find the value of : $^{n} C_{r} +^{n - 1} C_{r} + \dots +^{r} C_{r} = ?$

{n + 1}_{C_{r}}

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{n + 1}_{C_{r + 1}}

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{n + 2}_{C_{r}}

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2^{n}

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Solution

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Similar questions

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

^{n} C_{r} +^{n} C_{r - 1}

For $1 \leq r \leq n$ , the value of $ {}^nC_r +^{{}^{n-1}C_r}+^{{}^{n-2}C_r}.....+...+....+^{{}^rC_r} \space is : $

(2 \leq r \leq n),

^{n} C_{r} + 2 \cdot^{n} C_{r + 1} +^{n} C_{r + 2}

^{n} C_{r - 1} +^{n + 1} C_{r - 1} +^{n + 2} C_{r - 1} + . . . . . . . +^{2 n} C_{r - 1}, =^{2 n + 1} C_{r^{2} - 132} -^{n} C_{r}

r

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