Lt(x+x^(2)+x^(3)+.........+x^(n)-n)/(x-1)=

underset(x to 1)"Lt" (x+x^(2)+...+x^(n)-n)/(x-1)=

Let f(x)=x+(1-x)x^(3)+(1-x)(1-x^(2))x^(3)+.........+(1-x)(1-x^(2))......*(1-x^(n-1))x^(n);(n>=4) then :

Evaluate the following limits : Lt_(xto0)((1^(x)+2^(x)+.........+n^(x))/n)^(n/x)

if |x|<1 then (Lt)_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))......*(1+x^(2n))=

If |x| lt 1" thn "underset(n to oo)"Lt "(1+x)(1+x^(2))(1+x^(4))....(1+x^(2n))=

Let P(x) = a_(0) + a_(1)x^(2) + a_(2)x^(4) + ..........+ a_(n) x^(2n) be a polynomial in a real variable x with 0 lt a_(0) lt a_(1) lt a_(2) lt ……………. lt a_(n) The function P(x) has :

Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x^(n-1))x^n;(n >= 4) then :

If x_(1), x_(2),"……….",x_(n) are n non zero real numbers such that (x_(1)^(2) + x_(2)^(2) + "...."+x_(n-1)^(2))( x_(2)^(2) + x_(3)^(2) + x_(3)^(2) + "......" + x_(n)^(2))le ( x_(1) x_(2) + x_(2) x_(3)+"....."+x_(n-1)x_(n))^(2) , then x_(1) , x_(2) ,".....",x_(n) are in :

Coefficient of x^(n-1) in the expansion of.(x+3)^(n)+(x+3)^(n-1)(x+2)+(x+3)^(n-2)(x+2)^(2)+.........+(x+2)^(n) is :