If `a_(1),quad a_(2)quad .........+quad a_(n)` are the integers in the range of `f(x)=sqrt(9-|x-1|-2|x-4|-|x-2|),` then `sum_(i=1)^(n)a_(i)` equals:

Let a_(1),a_(2),.......,a_(n) be fixed real numbers and define a function f(x)=(x-a_(1))(x-a_(2)) ......(x-a_(n)) , what is lim f(x) ? For some anea_(1),a_(2),.........a_(n) , compute lim_(Xrarr1) f(x)

If a_(1),a_(2),a_(3) and a_(4) are first four terms of an increasing G.P. such that a_(i)in N AA i in N and sum_(i=1)^(4)a_(i)=4(a_(3)-a_(2))+32 ,then find the value of (a_(2)+(a_(4))/(a_(3)))

If n>=3 and a_(1),a_(2),a_(3),.....,a_(n-1) are n^(th) roots of unity,then the sum of sum_(1<=i

If a_(0), a_(1), a(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .

Consider (1 + x + x^(2))^(n) = sum_(r=0)^(n) a_(r) x^(r) , where a_(0), a_(1), a_(2),…, a_(2n) are real number and n is positive integer. If n is odd , the value of sum_(r-1)^(2) a_(2r -1) is

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

(1+x)^(n)=a_(0)+a_(1)x+a_(2)*x^(2)+......+a_(n)x^(n) then prove that

Let f(x)=(pi)/(4)+cos^(-1)((x)/(sqrt(1+x^(2))))tan^(-1)x and a_(i)(a_(i)a_(i+1)AA i=1,2,3,......,n) be the positive integral values of x for which sgn(f(x))=1, where sgn(y) denotes signum function ofy.Find sum_(i=1)^(n)a_(i)^(2)