ಒಂದು ಧನಾತ್ಮಕ ಪೂರ್ಣಾಂಕ `n ,` ಕ್ವಾಡ್ರಾಟಿಕ್ ಸಮೀಕರಣಕ್ಕಾಗಿ, `x(x+1)+(x-1)(x+2)++(x+ n-1)(x+n)=10 ...

If x+1/x=-2 then x^(2n+1)+1/(x)^(2n+1)=

n + (n-1) x + (n-2) x ^ (2) + ....... + 2x ^ (n-2) + x ^ (n-1)

AA n in N, 1 + 2x + 3x ^ (2) ++ ndot x ^ (n-1) = (x in R, x! = 1)

If,for a positive integer n,the quadratic equation,x(x+1)+(x+1)(x+2)+......+(x+bar(n)-1)(x+n)=10n has two consecutive integral solutions,then n is equal to

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

lim_ (n rarr oo) n ^ (2) (x ^ ((1) / (n)) - x ^ ((1) / (n + 1))), x> 0

lim_(x rarr2)((1+x)^(n)-3^(n))/(x-2)=n*3^(n-1)

The value of the determinant of n^(t h) order, being given by |x1 11x11 1x | is (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

Show that: (x)+(x+(1)/(n))+(x+(2)/(n))+...+(x+(n-1)/(n))=nx+(n-1)/(2)

lim_ (x rarr oo) ((1 ^ ((1) / (x)) + 2 ^ ((1) / (x)) + 3 ^ ((1) / (x)) ++ n ^ ((1 ) / (x))) / (n)) ^ (nx), n in N