If `underset(r=1)overset(n)Sigmar^4=I(n), " then "underset(r=1)overset(n)Sigma(2r -1)^4` is equal to

If Sigma_(r=1)^(n) r^4=I(n), " then "Sigma__(r=1)^(n) (2r -1)^4 is equal to

underset(r=0)overset(n)(sum)sin^(2)""(rpi)/(n) is equal to

If omega is a complex nth root of unity, then underset(r=1)overset(n)(ar+b)omega^(r-1) is equal to

Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset(10)sum tan^(-1) ((r)/(s))

Find the sum underset(r=1)r(r+1)(r+2)(r+3) .

The number of positive zeros of the polynomial underset(j=0)overset(n)(Sigma)^n C_r(-1)^r x^r is

Find the value of Sigma_(r=1)^(n) (a+r+ar)(-a)^r is equal to

Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .

Prove that underset(r = 0) overset (n)(sum) 3^(r) ""^(n)C_(r) = 4^(n)