" If "sum_(k=1)^(n-r)n-k_(c_(r))=x_(cy)" then "

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

If n in N, sum_(k=1)^(n)sin^(-1(x_(k))=(npi)/2 then the value of sum_(k=1)^(n)x_(k)=

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

If n in N, sum_(k=1)^(n)cos^(-1)(x_(k))=npi then the value of sum_(k=1)^(n)sin^(-1)(x_(k))=

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(n) and sum_(r=0)^(n)(C_(r))/(r+1)=k then the value of k is

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

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

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

Let S_(n)=sum_(r=1)^(oo)(1)/(n^(r)) and sum_(n=1)^(k)(n-1)S_(n)=5050, then k=