If `1+x^2=sqrt(3)x` ,then `sum_(n=1)^24(x^n-1/(x^n))` is equal to

If 1+x^(2)=sqrt(3)x , then sum_(n=1)^(24)(x^(n)-(1)/(x^n))^(2) is equal to

If 1+x^(2)=sqrt(3)x , then sum_(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

lim_(xto1) (sum_(r=1)^(n)x^(r)-n)/(x-1) is equal to

If x^(2) - x+ 1 =0, sum_(n=1)^(5) (x^(n) +(1)/(x^(n))) equals -

lim_(xrarr1) (sum_(x=1)^(n)x^(r)-n)/(x-1) is equal to

f(x)=(e^(x))/(e^(x)+sqrt(e)), the sum_(N=1)^(1-100)f'(N)-f'(1-N) is equal to,when N in Natural number

If sum_(i=1)^(2n) sin^(-1) x_i =npi , then sum_(i=1)^(2n) x_i is equal to :

If overlinex is the mean of a set of n observations x_1 , x_2 , x_3…..,x_n then sum_(i=1)^n(x_i-overlinex) is equal to

If [x] be the greatest integer less than or equal to x then sum_(n=8)^(100) [ ((-1)^n n)/(2)] is equal to :