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Show that,(1+5^(-1))(1+5^(-2))(1+5^(-4))...

Show that,`(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))=(5)/(4)(1-5^(-2(n+1)))`.

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`LHS=(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))`
`=(1+(1)/(5))(1+(1)/(5^(2)))(1+(1)/(5^(4)))"......."(1+(1)/(5^(2n)))`
`=((1-(1)/(5)))/((1-(1)/(5)))(1+(1)/(5))(1+(1)/(5^(2)))(1+(1)/(5^(4)))"......."(1+(1)/(5^(2n)))`
`=(5)/(4)[(1+(1)/(5^(2)))(1+(1)/(5^(2)))(1+(1)/(5^(4)))"......."(1+(1)/(5^(2n)))]`
`" " vdots " " vdots " "vdots" "`
`=(5)/(4)(1-(1)/(5^(2(n+1))))=(5)/(4)(1-5^(-2(n+1)))=RHS`.
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