The value of ""^(n)C(n)+""^(n+1)C(n)+""^...

The value of `""^(n)C_(n)+""^(n+1)C_(n)+""^(n+2)C_(n)+….+""^(n+k)C_(n)` :

A

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

B

`""^(n+k)C_(n)`

C

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

D

None of these

Verified by Experts

The correct Answer is:

A

The value of ""^(n)C(n)+""^(n+1)C(n)+""^(n+2)C(n)+….+""^(n+k)C(n) :
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C(0)^(n)C(n)^(n+1)+C(1)^(n)C(n-1)^(n)+C(2)^(n)*C(n-2)^(n-1)+.........+...
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Find the following sums : (i) .^(n)C(0)-.^(n)C(2)+.^(n)C(4)-.^(n)C(6...
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The value of (.^(n)C(0))/(n)+(.^(n)C(1))/(n+1)+(.^(n)C(2))/(n+2)+"..."...
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If the value of "^(n)C(0)+2*^(n)C(1)+3*^(n)C(2)+...+(n+1)*^(n)C(n)=576...
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Let (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r) and , (C(1))/(C(0)) + 2 (...
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If C(r) = ""^(n)C(r) and (C(0) + C(1)) (C(1) + C(2)) … (C(n-1) + C(n))...
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The value of (""^(n) C(1)+2. ""^(n) C(2)+3. ""^(n)C(3)+…+ n""^(n)C(n))...
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If (1+a)^(n)=.^(n)C(0)+.^(n)C(1)a+.^(n)C(2)a^(2)+ . . +.^(n)C(n)a^(n),...
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