If the continued fraction form of \( \frac{97}{19} \) is \( w+\frac{1}{x+\frac{1}{y}} \) where \( w, x, y \) are integers, then find the value of \( w+x+y \).
Given the continued form of
$\frac{97}{19}$ is $w + \frac{1}{x + \frac{1}{y}}$ where w, x, and y are integers.
To find the value of $w + x + y$
Solution:
The continued form of
$\frac{97}{19}$ = $5 + \frac{2}{19}$ = $5 + \frac{1}{\frac{19}{2}}$ = $5 + \frac{1}{9+ \frac{1}{2}}$ = $w + \frac{1}{x+ \frac{1}{y}}$
So comparing
$w = 5, x = 9, y = 2$
So $w + x + y = 5 + 9 + 2 = 16$ or
So, $w + x + y = 16$
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