For any real numbers a ,d`a*C_(0)+(a+d)C_(1)+(a+2d)C_(2)+ ____+(a+nd)*C_(n)=`

For any two real numbers C and D , cosC+cos D=

If C_(r) stands for nC_(r), then the sum of first (n+1) terms of the series aC_(0)-(a+d)C_(1)+(a+2d)C_(2)-(a+3d)C_(3)+...... is

If a,b,c,d are positive real numbers such that (a)/(3) = (a+b)/(4)= (a+b+c)/(5) = (a+b+c+d)/(6) , then (a)/(b+2c+3d) is:-

if a,b, c, d and p are distinct real number such that (a^(2) + b^(2) + c^(2))p^(2) - 2p (ab + bc + cd) + (b^(2) + c^(2) + d^(2)) lt 0 then a, b, c, d are in

If a, b, c and are real numbers and A =[{:( a,b),(c,d) :}] prove that A^(2) -(a+d) A+(ad-bc) I=0

Let a, b, c, d be real numbers such that sum_(k=1)^(n) (ak^(3) + bk^(2) + ck + d) = n^(4) or every natural number n. Then | a | + | b | + | C | + | d | is equal to

If a, b, c are distinct positive real numbers such that a+(1)/(b)=4,b+(1)/( c )=1,c+(1)/(d)=4 and d+(1)/(a)=1 , then