Given `x in (-1,0) uu (0,1) and f(x) = sum_(n=0)^oo x^n(-1)^((n(n+1))/2)` . The function f(x) is equivalent to a rational function -

sum_(n=0)^( oo) (-1)^(n) x^( n+1)=

If f(x)=sum_(n=0)^(oo)(x^(n))/(n!)(log a)^(n), then at x=0,f(x)

sum_ (n = 0) ^ (oo) (- 1) ^ (n) x ^ (n + 1) =

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1) then for x>0,y>0,f(xy) is equal to

The function (1n (1+x))/x "in" (0,oo) is

For x in Rwith|x|<1, the value of sum_(n=0)^(oo)(1+n)x^(n) is

The function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(|x|)-1) .

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

If f(x) = sum_(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)) , then the product of root of f(x) = 0 as n rarr oo , is