For 2- r - n- n-1 r- n r-1 - n r-2 is equal to-

The correct option is C ( ^n+2 _r) ^n+1C_r +^nC_r 1 +^nC_r 2 =^n+1C_r+^n+1C_r 1 =^n+2C_r ...

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Byju's Answer

Standard XII

Mathematics

Sum of Coefficients of All Terms

For 2≤ r ≤ ...

Question

For $2 \leq r \leq n, (_{r}^{n + 1}) + (_{r - 1}^{n}) + (_{r - 2}^{n})$ is equal to-

(_{r}^{n + 1})

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2 (_{r - 1}^{n + 1})

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2 (_{r}^{n + 2})

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(_{r}^{n + 2})

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Solution

The correct option is C $(_{r}^{n + 2})$
$^{n + 1} C_{r} +^{n} C_{r - 1} +^{n} C_{r - 2} =^{n + 1} C_{r} +^{n + 1} C_{r - 1} =^{n + 2} C_{r}$

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Similar questions

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then?

n \sum r = 0 r^{2} . (^{n} C_{r})^{2}

is equal to

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For 2≤r≤n,(n+1r)+(nr−1)+(nr−2) is equal to-

The correct option is C (n+2r)n+1Cr+nCr−1+nCr−2=n+1Cr+n+1Cr−1=n+2Cr

For $2 \leq r \leq n, (_{r}^{n + 1}) + (_{r - 1}^{n}) + (_{r - 2}^{n})$ is equal to-

The correct option is C $(_{r}^{n + 2})$
$^{n + 1} C_{r} +^{n} C_{r - 1} +^{n} C_{r - 2} =^{n + 1} C_{r} +^{n + 1} C_{r - 1} =^{n + 2} C_{r}$