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

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

If f(x)=lim_(n->oo)n(x^(1/n)-1),then for x >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

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

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

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1), then f or x>0,y>0,f(xy) is equal to : f(x)f(y) (b) f(x)+f(y)f(x)-f(y)(d) none of these

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

If x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n where |a|<1,|b|<1 then prove that sum_(n=0)^oo (ab)^n=(xy)/(x+y-1)

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

If x=sum_(n=0)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , then