`Limit_(n->oo) {(1+x) (1+x^2)(1+x^4).......(1+x^(2^n))}=` if `|x|<1` has the value equal to

if |x| oo)(1+x)(1+x^2)(1+x^4)........(1+x^(2n))=

Lim it_(n rarr oo){(1+x)(1+x^(2))(1+x^(4))......(1+x^(2^(n)))}= if |x|<1 has the value equal to

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

If |x|<1 , then lim_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))...(1+x^(2^n))=

f(x)=lim_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))..........(1+x^(2^(n-1))) then

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

f(n)=lim_(x->0){(1+sin(x/2))(1+sin(x/2^2)).......(1+sin(x/2^n))}^(1/x) then find lim_(n->oo)f(n)

lim_(x->oo)((1^(1/x) +2^(1/x) +3^(1/x) +...+n^(1/x))/n)^(nx) is equal to

lim_(x->oo)(1-x+x.e^(1/n))^n

Prove by mathematical induction that (1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+.....+(2^n)/(1+x^(2^n))=(1)/(x-1)+(2^(n+1))/(1-x^(2^(n+1))) where , |x|ne 1 and n is non - negative integer.