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`

If the graph of non-constant function is symmetric about the point (3,4), then the value of sum_(r=0)^(6)f(r)+f(3) is equal to

Let f(n)=sum_(r=0)^(n)sum_(k=r)^(n)([kr]). Also if f(n)=2047 ,then find the value of n

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If f(n)=sum_(r=1)^(n) r^(4) , then the value of sum_(r=1)^(n) r(n-r)^(3) is equal to

Let F(x)= F(x)=int_0^xtf(t)dt] and F(x^2)=x^4+x^5 then find the value of sum_(r=1)^12f(r^2)

Consider a twice differentiable function f(x) of degree four symmetrical to line x=1 defined as f:R rarr R and f'(2)=0. (A) The Sum of the roots of the cubic f'(x)=0 (i)

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

If the sum of the series sum_(n=0)^(oo)r^(n),|r|<1 is s then find the sum of the series sum_(n=0)^(oo)r^(2n)

Let f(x)=(r-2)(r+1)x^(2)+r(r-2)x-r(r-2)=0, where r in I,x in R. If roots of the equation f(x_(i)) are real and sum_(i=1)^(3)(f(x_(i)))^(2)=0, then the value of r is