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Show that sqrt(3)=1+1/3+1/3dot3/6+1/3dot...

Show that `sqrt(3)=1+1/3+1/3dot3/6+1/3dot3/6dot5/9+1/3dot3/6dot5/9dot7/(12)+`

Text Solution

Verified by Experts

`sqrt(3) = (1/3)^(-1//2)`
`= (1-2/3)^(-1//2)`
`= +(-1/2)(-2/3)+((-1/2)(-1/2-1))/(2!) (-2/3)^(2)+((-1/2)(-1/2-1)(-1/2-2))/(3!) (-2/3)^(3) + "....."`
`= 1+1/2.(2)/(3)+1/2.(3/2).(2/3)^(2).(1)/(2)+1/2.(3)/(2).(5)/(2).(2/3)^(3).(1)/(3!)+"....."`
`= 1+1/3+1/3(3/6)+(1)/(3)(3/6)(5/9)+"...."`
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