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lim(x-gtoo)(1+1/2+1/4+.....................

`lim_(x-gtoo)(1+1/2+1/4+...................+1/(2^x))`

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lim_(x rarr oo)(1+(1)/(2)+(1)/(4)+...+(1)/(2^(x)))=

lim_(xto1/2)|2x-1|/(2x-1)

lim_(xrarroo) (2x)/(1+4x)

lim_(xrarroo) (2x)/(1+4x)

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

lim_(x to 1)((1+x)/(2+x))^(1/2)

Prove that, lim_(xtooo)((1)/(4)+(1)/(4^(2))+(1)/(4^(3))+.......+(1)/(4^(x)))=(1)/(3)

lim_(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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