The value of `sum_(r=1)^5(x^r + 1/(x^r))^2, where x^2+x+1 = 0 is:- `

The value of sum_(r=1)^(18) cos^(2)(5r)^(@) , where x^(@) denotes the x degree, is equal to

The value of sum_(r=1)^(18) cos^(2)(5r)^(@) , where x^(@) denotes the x degree, is equal to

The value of sum_(r=1)^(18) cos^(2)(5r)^(@) , where x^(@) denotes the x degree, is equal to

If x^(2)+x+1=0 then find the value of sum_(r=1)^(27)(x^(r)+(1)/(x^(r)))^(2)

If x^(2)-x+1=0, then the value of sum_(r=1)^(2010)(x^(r)-(1)/(x^(r)))^(3) is equal to

Evaluate : sum_(r=1)^oo r^2x^(r-1),(|x|<1) .

The value of sum_(r=1)^n1/(sqrt(a+r x)+sqrt(a+(r-1)x)) is -

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-