Suppose x sqrt2sqrt2sqrt2 exist and is a positive number Fi

Suppose x = sqrt2+sqrt2+sqrt2+.... exist and is a positive number. Find x. Hint: Turn the equation into a square root equation.

Case 1: 2 recurs a finite number of times, say n. Then x = n 2 which is a positive number since both n and 2 are positive numbers.

Case 2: 2 is repeated an infinite number of times. Then x = as 2 is positive and the sum of a series of the same positive number repeated an infinite number of times is .