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 sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

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

If A=pi/5, then find the value of sum_(r=1)^8tan(r A)*tan((r+1)A)dot

If sum_(r=1)^n T_r=n(2n^2+9n+13), then find the sum sum_(r=1)^nsqrt(T_r)dot

Consider the function: f(x)=m a xdot{1,|x-1|, min {4,|3x-1|}}AAx in R . Then find the value of f(3)dot

If T_r=r(r^2-1), then find sum_(r=2)^oo1/Tdot

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

The value of sum_(r=0)^n(a+r+a r)(-a)^r is equal to

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.