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Write the expression \ ^n C(r+1)+\ ^n C(...

Write the expression `\ ^n C_(r+1)+\ ^n C_(r-1)+2xx\ ^n C_r` in the simplest form.

A

`""^(n+2)C_(r)`

B

`""^(n+2)C_(r+1)`

C

`""^(n+1)C_(r)`

D

`""^(n+1)C_(r+1)`

Text Solution

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The correct Answer is:
B
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If ""^(n)C _r denotes the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C_(r+1)

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C _(r+1)

If ""^(n)C _4 denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2)C_(r+1)

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

If ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.

""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

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