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Find the value of 2+1/(2+1/(2+1/(2+oo)))...

Find the value of `2+1/(2+1/(2+1/(2+oo)))`

Text Solution

Verified by Experts

The correct Answer is:
1 + sqrt(2)`,
Let the given expression be equal to x . Them
`x = 2+(1)/(x)`
or `x^(2)-2x - 1 = 0`
or `x= (2pmsqrt(4+ 4))/(2) = (2pm2 sqrt(2))/(2) = 1 pm sqrt(2)`
But, the given expression is positive. Therefore, ` x = 1 + sqrt(2)` is the value of the given expression
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