[" 11.If "x in(-1,0)uu(0,1)" and "f(x)=sum_(n=0)^(oo)x^(n)*(-1)^((n(n+1))/(2))],[" Then,the function,"f(x)" is equivalent to a rational "],[" function "]

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

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 (a) (1-x)/(1+x^(2)) (b) (1+x)/(1+x^(2)) (c) (1)/(1-x) (d) (1)/(1+x)

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) = 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

If f(x)=sum_(lambda=1)^(n)(x-(5)/(lambda))(x-(4)/(lambda+1)) then lim_(n rarr oo)f(0) is equal to

If f(x)=sum_(lambda=1)^(n)(x-(5)/(lambda))(x-(4)/(lambda+1)) then lim_(n rarr oo)f(0) is equal to

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