If `(1+a)(1+a^(2))(1+a^(4)) . . . . (1+a^(128))=underset(r=0)overset(n)suma^(r )`, then n is equal to

If (1+a)(1+a^(2))(1+a^(4)) . . . . (1+a^(128))=sum_(r=0)^(n) a^(r ) , then n is equal to

underset(r=1)overset(n)sum ( r )/(r^(4)+r^(2)+1) is equal to

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

sum_(r=1)^n r (n-r +1) is equal to :

If T_( r )=( r )/(r^(4)+4) and S_(n)=underset(r=1)overset(n)sum t_( r ) . Then the value of 37S_(5)-(7)/(26) is equal to

If n is a positive integer and if (1+x+x^(2))^(2n)=underset(r=0)overset(2n)(sum)a_(r)x^(r) , then

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

If k=underset(r=0)overset(n)(sum)(1)/(.^(n)C_(r)) , then underset(r=0)overset(n)(sum)(r)/(.^(n)C_(r)) is equal to