If the sum of `1+2r+3r^2+4r^3+...oo9/16`,find the value of r.

If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then value of r is (a) 1//2 b. 1//3 c. 1//4 d. none of these

If the coefficients of the (r-1) th and (2r+3) th terms in the equation of (1+x)^(15) are equal, find the value of r.

If the coffcients of the (4r+5) ans (2r+1) th terms in the expansion of (1+x)^(10) are equal , find the value of r .

If the binomial coefficient of the (2r+4)^(th) term and (r-2)^(th) term in the expansion of (1+x)^(18) are equal find the value of r.

If 1/( ^5C_r)+1/( ^6C_r)+1/(~^4C_r) find the value of r.

If z_r : r=1,2,3, ,50 are the roots of the equation sum_(r=0)^(50)z^r=0 , then find the value of sum_(r=0)^(50)1/(z_r-1)

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If R_(1) is the circumradius of the pedal triangle of a given triangle ABC, and R_(2) is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4) ..., then the value of underset( i=1)overset(oo)sum R_(i) , where R (circumradius) of DeltaABC is 5 is

If 16C_r=^16C_(2r+1) then the value of r will be

An odd function is symmetric about the vertical line x=a ,(a >0),a n dif sum_(r=0)^oo[f(1+4r]^r=8, then find the value of f(1)dot