Find out the range of the following `2/(x^n+x^(n-1)+x^(n-2)+....+1/(n^n)),` where `x in R^+.`

int(x-a)(x^(n-1)+x^(n-2)a+...+a^(n-1))dx where n is +ve integer =

Find the derivative of x^(n)+ax^(n-1)1+a^(2)x^(n-2)+...+a^(n-1)x+a^(n) for some fixed real number a.

Find the sum to n terms of the series n+(n-1)x+(n-2)x^(2)+.........+2x^(n-2)+x^(r)

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

Find the coefficient of x^(r) in the following expression : (x+n)^(n)+(x+2)^(n-1)(x+1)+(x+2)^(n-2)(x+1)^(2)+.....+(x+1)^(n)

Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n !))^2 .

The value of lim_(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x)))/(x^(n)) (where n in N ) is

The value of lim_(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x)))/(x^(n)) (where n in N ) is

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function) then which of the following is correct a. n (b) 1 (c) 1/n (d) none of these