" 20."" If "sum_(k=1)^(n-r)n-k_(r)=^(x)C_(y)" then "

If {:("n-r"),( sum),("k=1"):} .^(n-k)C_(r)=.^(x)C_(y) then

If sum_(k=1)^(n+1)hat imath(n-k)C_(r)=x_(y) then x=n and y=r+1

Prove that sum_(k=1)^(n-r ) ""^(n-k)C_(r )= ""^(n)C_( r+1) .

(n)p_(r)=k^(n)C_(n-r),k=

The value of sum_(r=1)^(n+1)(sum_(k=1)^(k)C_(r-1))( where r,k,n in N) is equal to a.2^(n+1)-2b2^(n+1)-1c.2^(n+1)d. none of these

Statement : if n in Nandn is not a multiple of 3 and (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then the value of sum_(r=0)^(n)(-1)^(r)ar^(n)C_(r) is zero Statement 2: The cofficient of x^(n) in the expansion of n=3k+1 or n=3k+2

If sum_(r=1)^(n)t_(r)=sum_(k=1)^(n)sum_(j=1)^(k)sum_(i=1)^(j)2, then sum_(r=1)^(n)(1)/(t_(r))=

If sum_(j=0)^(2015)sum_(i=0)^(2015)iC_(j)=k, then the value of (k+2)^((1)/(216))is(where^(n)C_(r)=0AA n