If `underset(r=1)overset(10)sum r! (r^(3)+6r^(2)+2r+5)=alpha (11!)`, then the value of `alpha` 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

If alpha=(pi)/(13) then the value of prod_(r=1)^(6)cos r alpha is equal to

Let ""^(n)C_(r) denote the binomial coefficient of x^(r) in the expansion of (1+x)^(n) . If underset(k=0)overset(10)sum (2^(2)+3k) ""^(n)C_(k)=alpha 3^(10)+beta. 2^(10), alpha, beta in R then alpha+beta is equal to..........

If sum_(0)^(10) 5/((r+2)(r+4)) is alpha . Then, find the value of [alpha] .

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 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